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4.07 Graphical solutions to linear equations or inequalities

Interactive practice questions

Consider the equation $\frac{3x}{5}-1=2$3x51=2.

a

Solve for the value of $x$x that satisfies the equation.

b

To verify the solution graphically, which two straight lines would need to be graphed?

$y=\frac{3x}{5}$y=3x5

A

$y=\frac{3x}{5}+1$y=3x5+1

B

$y=2$y=2

C

$y=\frac{3x}{5}-1$y=3x51

D
c

Graph the lines $y=\frac{3x}{5}-1$y=3x51 and $y=2$y=2 on the same plane.

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d

Hence find the value of $x$x that satisfies the two equations $y=\frac{3x}{5}-1$y=3x51 and $y=2$y=2 simultaneously.

Easy
5min

Consider the equation $2\left(x-1\right)-3=7$2(x1)3=7.

Easy
4min

Consider the equation $2x=8-2x$2x=82x.

Easy
4min

Consider the equation $4x+3=2x-1$4x+3=2x1.

Easy
4min
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Outcomes

I.A.REI.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) =g(x); find the solutions approximately. Include cases where f(x) and/or g(x) are linear and exponential functions.

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