Writing Equations 3
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Question 1 of 4
1. Question
If the sum of a number and `5` is multiplied by `3`, the answer is the same as twice the number plus `26`. What is the number?- (11)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.Number`=n`If the sum of a number and `5` is multiplied by `3`, the answer is the same as twice the number plus `26` `n+5` `times` `3` `=` `2times` `n` `+` `26` Simplify the equation:`(n+5)times3` `=` `(2timesn)+26` `3(n+5)` `=` `2n+26` To solve for `n`, it needs to be alone on one side.Start by expanding the left side of the equation by using the Distributive Property.`3``(``n` `+5)` `=` `2``n` `+26` `3``n` `+``3``(5)` `=` `2``n` `+26` `3``n` `+15` `=` `2``n` `+26` Next, move `2n` to the other side by subtracting `2n` from both sides of the equation.`3``n` `+15` `=` `2``n` `+26` `3``n` `+15` `-2n` `=` `2``n` `+26` `-2n` `n` `+15` `=` `26` `2n-2n` cancels out Finally, move `15` to the other side by subtracting `15` from both sides of the equation.`n` `+15` `=` `26` `n` `+15` `-15` `=` `26` `-15` `n` `=` `11` `15-15` cancels out The number is `11`.Check our workTo confirm our answer, substitute `n=11` to the original equation.`3(n+5)` `=` `2n+26` `3(11+5)` `=` `2(11)+26` Substitute `n=11` `3(16)` `=` `22+26` `48` `=` `48` Since the equation is true, the answer is correct.`11` -
Question 2 of 4
2. Question
A number is divided by `5` plus `3` equals twice the number and `12`. What is the number?- (-5)
Hint
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Great Work!
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.Number`=n`A number is divided by `5` plus `3` equals twice the number and `12` `n` `divide` `5` `+` `3` `=` `2times` `n` `+` `12` Simplify the equation:`(ndivide5)+3` `=` `(2timesn)+12` `n/5 +3` `=` `2n+12` To solve for `n`, it needs to be alone on one side.Start by removing `1/5` by multiplying both sides of the equation by `5`.$$\frac{\color{#00880A}{n}}{5}+3$$ `=` `2``n``+12` $$\left(\frac{\color{#00880A}{n}}{5}+3\right)\color{#CC0000}{\times5}$$ `=` `(2``n``+12)``times5` `n` `+15` `=` `5(2``n` `+12)` `1/5times5` cancels out Next, expand the right side of the equation using the Distributive Property.`n` `+15` `=` `5``(2``n` `+12)` `n` `+15` `=` `5``(2``n``)+``5``(12)` `n` `+15` `=` `10``n``+60` Now, move `n` to the other side by subtracting `n` from both sides of the equation.`n` `+15` `=` `10``n``+60` `n` `+15` `-n` `=` `10``n``+60` `-n` `15` `=` `9``n` `+60` `n-n` cancels out Then, move `60` to the other side by subtracting `60` from both sides of the equation.`15` `=` `9``n` `+60` `15` `-60` `=` `9``n` `+60` `-60` `-45` `=` `9``n` `60-60` cancels out Finally, remove `9` by dividing both sides of the equation by `9`.`-45` `=` `9``n` `-45``divide9` `=` `9``n``divide9` `-5` `=` `n` `9divide9` cancels out `n` `=` `-5` The number is `-5`.Check our workTo confirm our answer, substitute `n=-5` to the original equation.`n/5 +3` `=` `2n+12` `(-5)/5 +3` `=` `2(-5)+12` Substitute `n=-5` `-1+3` `=` `-10+12` `2` `=` `2` Since the equation is true, the answer is correct.`-5` -
Question 3 of 4
3. Question
The sum of a number and `3` is multiplied by `5`. The answer is the same as `3` times the number plus `21`. What is the number?- (3)
Hint
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Good Job!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Distributive Property
`a``(b+c)=``a``b+``a``c`Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.Number`=x`The sum of a number and `3` is multiplied by `5`. The answer is the same as `3` times the number plus `21` `x+3` `times` `5` `=` `3` `times` `x` `+` `21` Simplify the equation:`(x+3)times5` `=` `(3timesx)+21` `5(x+3)` `=` `3x+21` To solve for `x`, it needs to be alone on one side.Start by expanding the left side of the equation using the Distributive Property.`5``(``x` `+3)` `=` `3``x` `+21` `5``x` `+``5``(3)` `=` `3``x` `+21` `5``x` `+15` `=` `3``x` `+21` Now, move `3x` to the other side by subtracting `3x` from both sides of the equation.`5``x` `+15` `=` `3``x` `+21` `5``x` `+15` `-3x` `=` `3``x` `+21` `-3x` `2``x` `+15` `=` `21` `3x-3x` cancels out Then, move `15` to the other side by subtracting `15` from both sides of the equation.`2``x` `+15` `=` `21` `2``x` `+15` `-15` `=` `21` `-15` `2``x` `=` `6` `15-15` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`2``x` `=` `6` `2``x``divide2` `=` `6``divide2` `x` `=` `3` `2divide2` cancels out The number is `3`.`3` -
Question 4 of 4
4. Question
The sum of `3` consecutive numbers is `36`. What are the numbers?-
`1`st number `=` (11)`2`nd number `=` (12)`3`rd number `=` (13)
Hint
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Fantastic!
Incorrect
Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Keywords for Word Problems Keyword Meaning Certain number Unknown variable (`x,y,z,` etc) is the same as, The answer is, is equal `=` sum, and, plus, more than `+` subtracted, less, minus `-` times, product, multiplied, twice `times` half of, divide by `divide` First, label the values and form an equation using the information given.`1`st number`=x``2`nd number`=x+1` (since it comes after the `1`st number)`3`rd number`=x+2` (since it comes after the `2`nd number)The sum of three consecutive numbers is `36` `x+x+1+x+2` `=` `36` Simplify the equation:`x+x+1+x+2` `=` `36` `3x+3` `=` `36` To solve for `x`, it needs to be alone on one side.Start by moving `3` to the other side by subtracting `3` from both sides of the equation.`3``x` `+3` `=` `36` `3``x` `+3` `-3` `=` `36` `-3` `3``x` `=` `33` `3-3` cancels out Next, remove `3` by dividing both sides of the equation by `3`.`3``x` `=` `33` `3``x``divide3` `=` `33``divide3` `x` `=` `11` `3divide3` cancels out Substitute `x=11` to find each number.`1`st number `=` `x` `=` `11` `2`nd number `=` `x` `+1` `=` `11` `+1` `=` `12` `3`rd number `=` `x` `+2` `=` `11` `+2` `=` `13` Check our workTo confirm our answer, add the `3` numbers and check if the sum is `36`.`11+12+13` `=` `36` `36` `=` `36` Since the equation is true, the answer is correct.`1`st number `=11``2`nd number `=12``3`rd number `=13` -
Quizzes
- One Step Equations – Add and Subtract 1
- One Step Equations – Add and Subtract 2
- One Step Equations – Add and Subtract 3
- One Step Equations – Add and Subtract 4
- One Step Equations – Multiply and Divide 1
- One Step Equations – Multiply and Divide 2
- One Step Equations – Multiply and Divide 3
- One Step Equations – Multiply and Divide 4
- Two Step Equations 1
- Two Step Equations 2
- Two Step Equations 3
- Two Step Equations 4
- Multi-Step Equations 1
- Multi-Step Equations 2
- Solve Equations using the Distributive Property 1
- Solve Equations using the Distributive Property 2
- Solve Equations using the Distributive Property 3
- Equations with Variables on Both Sides 1
- Equations with Variables on Both Sides 2
- Equations with Variables on Both Sides 3
- Equations with Variables on Both Sides (Fractions) 1
- Equations with Variables on Both Sides (Fractions) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 1
- Solve Equations – Variables on Both Sides (Distributive Property) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 3
- Solve Equations – Variables on Both Sides (Distributive Property) 4
- Writing Equations 1
- Writing Equations 2
- Writing Equations 3
- Writing Equations 4
- Equation Word Problems (Age) 1
- Equation Word Problems (Money) 1
- Equation Word Problems (Harder) 1
- Equation Problems with Substitution 1
- Equation Problems (Geometry) 1
- Equation Problems (Geometry) 2
- Equation Problems (Perimeter)
- Equation Problems (Area)
- Solve for a Variable or Formula 1
- Solve for a Variable or Formula 2
- Solve for a Variable or Formula 3