5.4 Solve equations with decimals

$x-0.8=2.3$
ⓐ $x=2$ ⓑ $x=\mathrm{-1.5}$ ⓒ $x=3.1$

$y+0.6=\mathrm{-3.4}$
ⓐ $y=\mathrm{-4}$ ⓑ $y=\mathrm{-2.8}$ ⓒ $y=2.6$

$\frac{h}{1.5}=\mathrm{-4.3}$
ⓐ $h=6.45$ ⓑ $h=\mathrm{-6.45}$ ⓒ $h=\mathrm{-2.1}$

$0.75k=\mathrm{-3.6}$
ⓐ $k=\mathrm{-0.48}$ ⓑ $k=\mathrm{-4.8}$ ⓒ $k=\mathrm{-2.7}$

$y+2.9=5.7$

$m+4.6=6.5$

$f+3.45=2.6$

$h+4.37=3.5$

$a+6.2=\mathrm{-1.7}$

$b+5.8=\mathrm{-2.3}$

$c+1.15=\mathrm{-3.5}$

$d+2.35=\mathrm{-4.8}$

$n-2.6=1.8$

$p-3.6=1.7$

$x-0.4=\mathrm{-3.9}$

$y-0.6=\mathrm{-4.5}$

$j-1.82=\mathrm{-6.5}$

$k-3.19=\mathrm{-4.6}$

$m-0.25=\mathrm{-1.67}$

$q-0.47=\mathrm{-1.53}$

$0.5x=3.5$

$0.4p=9.2$

$\mathrm{-1.7}c=8.5$

$\mathrm{-2.9}x=5.8$

$\mathrm{-1.4}p=\mathrm{-4.2}$

$\mathrm{-2.8}m=\mathrm{-8.4}$

$\mathrm{-120}=1.5q$

$\mathrm{-75}=1.5y$

$0.24x=4.8$

$0.18n=5.4$

$\mathrm{-3.4}z=\mathrm{-9.18}$

$\mathrm{-2.7}u=\mathrm{-9.72}$

$\frac{a}{0.4}=\mathrm{-20}$

$\frac{b}{0.3}=\mathrm{-9}$

$\frac{x}{0.7}=\mathrm{-0.4}$

$\frac{y}{0.8}=\mathrm{-0.7}$

$\frac{p}{-5}=\mathrm{-1.65}$

$\frac{q}{-4}=\mathrm{-5.92}$

$\frac{r}{-1.2}=\mathrm{-6}$

$\frac{s}{-1.5}=\mathrm{-3}$

$x-5=\mathrm{-11}$

$-\frac{2}{5}=x+\frac{3}{4}$

$p+8=\mathrm{-2}$

$p+\frac{2}{3}=\frac{1}{12}$

$\mathrm{-4.2}m=\mathrm{-33.6}$

$q+9.5=\mathrm{-14}$

$q+\frac{5}{6}=\frac{1}{12}$

$\frac{8.6}{15}=-d$

$\frac{7}{8}m=\frac{1}{10}$

$\frac{j}{-6.2}=\mathrm{-3}$

$-\frac{2}{3}=y+\frac{3}{8}$

$s-1.75=\mathrm{-3.2}$

$\frac{11}{20}=-f$

$\mathrm{-3.6}b=2.52$

$\mathrm{-4.2}a=3.36$

$\mathrm{-9.1}n=\mathrm{-63.7}$

$r-1.25=\mathrm{-2.7}$

$\frac{1}{4}n=\frac{7}{10}$

$\frac{h}{-3}=\mathrm{-8}$

$y-7.82=\mathrm{-16}$

The sum of $n$ and $\mathrm{-7.3}$ is $\mathrm{2.4.}$

The sum of $n$ and $\mathrm{-5.1}$ is $3.8.$

Shawn bought a pair of shoes on sale for $\mathrm{\$78}$ . Solve the equation $0.75p=78$ to find the original price of the shoes, $p.$

Mary bought a new refrigerator. The total price including sales tax was $\text{\$1,350}.$ Find the retail price, $r,$ of the refrigerator before tax by solving the equation $1.08r=\mathrm{1,350}.$

Think about solving the equation $1.2y=60,$ but do not actually solve it. Do you think the solution should be greater than $60$ or less than $60?$ Explain your reasoning. Then solve the equation to see if your thinking was correct.

Think about solving the equation $0.8x=200,$ but do not actually solve it. Do you think the solution should be greater than $200$ or less than $200?$ Explain your reasoning. Then solve the equation to see if your thinking was correct.