By substituting into the equation, identify whether the following statements are true or false.
$x=5$x=5 is a solution for the equation $4x-2=18$4x−2=18.
$x=4$x=4 is a solution for the equation $6x-13=12$6x−13=12.
$x=4$x=4 is a solution for the equation $5x+12=31$5x+12=31.
$x=2$x=2 is a solution for the equation $3x+1=7$3x+1=7.
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.