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

Solving two-step linear equations using distributive property: a(x+b)=c\;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.

Lessons

  • 1.
    Solve the equation using model.
    a)
    4(x+1)=124\left( {x + 1} \right) = 12

    b)
    2(x3)=82\left( {x - 3} \right) = 8


  • 2.
    Solve.
    a)
    3(x9)=453\left( {x - 9} \right) = 45

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

    c)
    15=3(x6) - 15 = 3\left( {x - 6} \right)

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


  • 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.