4. Equations & Inequalities

By substituting into the equation, identify whether the following statements are true or false.

a

$x=5$`x`=5 is a solution for the equation $4x-2=18$4`x`−2=18.

True

A

False

B

True

A

False

B

b

$x=4$`x`=4 is a solution for the equation $6x-13=12$6`x`−13=12.

True

A

False

B

True

A

False

B

c

$x=4$`x`=4 is a solution for the equation $5x+12=31$5`x`+12=31.

True

A

False

B

True

A

False

B

d

$x=2$`x`=2 is a solution for the equation $3x+1=7$3`x`+1=7.

True

A

False

B

True

A

False

B

Easy

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Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

(a) Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.