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

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

Continue from the previous section, we will solve linear equations in diagram, equation, and word problems forms. However, in addition to subtraction and addition, we will teach you how to solve linear equations that also involve multiplications and divisions.
Basic Concepts: Dividing integers, Model and solve one-step linear equations: ax=bax = b, xa=b\frac{x}{a} = b, Solving two-step linear equations using addition and subtraction: ax+b=cax + b = c
Related Concepts: Solving linear equations using multiplication and division, Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c, Solving linear equations using distributive property: a(x+b)=ca(x + b) = c, Solving linear equations with variables on both sides

Lessons

  • 1.
    Find x in the equation modelled by each diagram.
    a)

    Solving two-step linear equations using multiplication and division

    b)

    model and solve two-step linear equations using multiplication and division

  • 2.
    Solve.
    a)
    3+x4=513 + \frac{x}{4} = 51

    b)
    17=10+x−217 = 10 + \frac{x}{{ - 2}}

    c)
    x−6−21=−9\frac{x}{{ - 6}} - 21 = - 9

    d)
    −1=23+x8 - 1 = 23 + \frac{x}{8}

  • 3.
    The amount of time needed for an ice cube to melt when the temperature is between 10 °C to 30 °C can be expressed by the equation t=16−C2t = 16 - \frac{C}{2}, where t is the amount of time for the ice cube to melt in minute; and C is the temperature in degree Celsius.
    a)
    Will the ice melt in 10 minutes if the temperature is 10 °C?

    b)
    What was the lowest temperature for the ice cube to melt in 5 minutes?

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23.
Solving Linear Equations
23.1
Model and solve one-step linear equations: ax=bax = b, xa=b\frac{x}{a} = b
23.2
Solving two-step linear equations using addition and subtraction: ax+b=cax + b = c
23.3
Solving two-step linear equations using multiplication and division: xa+b=c\frac{x}{a} + b = c
23.4
Solving two-step linear equations using distributive property: a(x+b)=c\;a\left( {x + b} \right) = c
UK Year 9 Maths
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