Solving two-step linear equations using distributive property: $\;a\left( {x + b} \right) = c$ - Basic Algebra

Solving two-step linear equations using distributive property: $\;a\left( {x + b} \right) = c$

Distributive property is an algebra property that we use all the time! When you see equations in the form of a(x+b), you can transform them into ax+ab by multiplying the terms inside a set of parentheses. In this section, we will make use of this property to help us solve linear equations.

Basic concepts:
Model and solve one-step linear equations: $ax = b$ , $\frac{x}{a} = b$
Solving two-step linear equations using addition and subtraction: $ax + b = c$
Solving two-step linear equations using multiplication and division: $\frac{x}{a} + b = c$

Related concepts:
Solving linear equations using multiplication and division
Solving two-step linear equations: $ax + b = c$ , ${x \over a} + b = c$
Solving linear equations using distributive property: $a(x + b) = c$
Solving linear equations with variables on both sides

Lessons

1.
Solve the equation using model.
2.
Solve.
3.
John has a round table with a circumference of 314.16 cm, but it is too big for his new home. So, he cut off a 10 cm wide border around the edge.

Solving two-step linear equations using distributive property: $\;a\left( {x + b} \right) = c$

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AlgebraModel and solve one-step linear equations: ax=bax = bax=b, xa=b\frac{x}{a} = b​a​​x​​=b

AlgebraSolving two-step linear equations using addition and subtraction: ax+b=cax + b = cax+b=c

AlgebraSolving two-step linear equations using multiplication and division: xa+b=c\frac{x}{a} + b = c​a​​x​​+b=c

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Model and solve one-step linear equations: ax=bax = bax=b, xa=b\frac{x}{a} = b​a​​x​​=b

Solving two-step linear equations using addition and subtraction: ax+b=cax + b = cax+b=c

Solving two-step linear equations using multiplication and division: xa+b=c\frac{x}{a} + b = c​a​​x​​+b=c

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Lesson: 1b

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Intro

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Practice

Do better in math today

Don't just watch, practice makes perfect.

Do better in math today

Don't just watch, practice makes perfect.

Lessons

1.

Solve the equation using model.

a)

4(x+1)=124\left( {x + 1} \right) = 124(x+1)=12

b)

2(x−3)=82\left( {x - 3} \right) = 82(x−3)=8

2.

Solve.

a)

3(x−9)=453\left( {x - 9} \right) = 453(x−9)=45

b)

7(10+x)=147\left( {10 + x} \right) = 147(10+x)=14

c)

−15=3(x−6) - 15 = 3\left( {x - 6} \right)−15=3(x−6)

d)

−22=11(x+13) - 22 = 11\left( {x + 13} \right)−22=11(x+13)

3.

John has a round table with a circumference of 314.16 cm, but it is too big for his new home. So, he cut off a 10 cm wide border around the edge.

a)

Write the equation that represents the situation.

b)

What is the circumference of the table now? Round your answer to two decimal places.

Solving two-step linear equations using distributive property: a(x+b)=c\;a\left( {x + b} \right) = ca(x+b)=c

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Algebra
Model and solve one-step linear equations: $ax = b$ , $\frac{x}{a} = b$

Algebra
Solving two-step linear equations using addition and subtraction: $ax + b = c$

Algebra
Solving two-step linear equations using multiplication and division: $\frac{x}{a} + b = c$

Model and solve one-step linear equations: $ax = b$ , $\frac{x}{a} = b$

Solving two-step linear equations using addition and subtraction: $ax + b = c$

Solving two-step linear equations using multiplication and division: $\frac{x}{a} + b = c$

or

$4\left( {x + 1} \right) = 12$

$2\left( {x - 3} \right) = 8$

$3\left( {x - 9} \right) = 45$

$7\left( {10 + x} \right) = 14$

$- 15 = 3\left( {x - 6} \right)$

$- 22 = 11\left( {x + 13} \right)$

Solving two-step linear equations using distributive property: $\;a\left( {x + b} \right) = c$