Chapter Practice Test

Determine Whether a Decimal is a Solution of an Equation In the following exercises, determine whether each number is a solution of the given equation.

[latex]x - 0.8=2.3[/latex]

ⓐ [latex]x=2[/latex] ⓑ [latex]x=-1.5[/latex] ⓒ [latex]x=3.1[/latex]

ⓐ no ⓑ no ⓒ yes

[latex]y+0.6=-3.4[/latex]

ⓐ [latex]y=-4[/latex] ⓑ [latex]y=-2.8[/latex] ⓒ [latex]y=2.6[/latex]

[latex]\Large\frac{h}{1.5}\normalsize =-4.3[/latex]

ⓐ [latex]h=6.45[/latex] ⓑ [latex]h=-6.45[/latex] ⓒ [latex]h=-2.1[/latex]

ⓐ no ⓑ yes ⓒ no

[latex]0.75k=-3.6[/latex]

ⓐ [latex]k=-0.48[/latex] ⓑ [latex]k=-4.8[/latex] ⓒ [latex]k=-2.7[/latex]

Solve Equations with Decimals

In the following exercises, solve the equation.

[latex]y+2.9=5.7[/latex]

y = 2.8

[latex]m+4.6=6.5[/latex]

[latex]f+3.45=2.6[/latex]

f = −0.85

[latex]h+4.37=3.5[/latex]

[latex]a+6.2=-1.7[/latex]

a = −7.9

[latex]b+5.8=-2.3[/latex]

[latex]c+1.15=-3.5[/latex]

c = −4.65

[latex]d+2.35=-4.8[/latex]

[latex]n - 2.6=1.8[/latex]

n = 4.4

[latex]p - 3.6=1.7[/latex]

[latex]x - 0.4=-3.9[/latex]

x = −3.5

[latex]y - 0.6=-4.5[/latex]

[latex]j - 1.82=-6.5[/latex]

j = −4.68

[latex]k - 3.19=-4.6[/latex]

[latex]m - 0.25=-1.67[/latex]

m = −1.42

[latex]q - 0.47=-1.53[/latex]

[latex]0.5x=3.5[/latex]

x = 7

[latex]0.4p=9.2[/latex]

[latex]-1.7c=8.5[/latex]

c = −5

[latex]-2.9x=5.8[/latex]

[latex]-1.4p=-4.2[/latex]

p = 3

[latex]-2.8m=-8.4[/latex]

[latex]-120=1.5q[/latex]

q = −80

[latex]-75=1.5y[/latex]

[latex]0.24x=4.8[/latex]

x = 20

[latex]0.18n=5.4[/latex]

[latex]-3.4z=-9.18[/latex]

z = 2.7

[latex]-2.7u=-9.72[/latex]

[latex]\Large\frac{a}{0.4}\normalsize =-20[/latex]

a = −8

[latex]\Large\frac{b}{0.3}\normalsize =-9[/latex]

[latex]\Large\frac{x}{0.7}\normalsize =-0.4[/latex]

x = −0.28

[latex]\Large\frac{y}{0.8}\normalsize =-0.7[/latex]

[latex]\Large\frac{p}{-5}\normalsize =-1.65[/latex]

p = 8.25

[latex]\Large\frac{q}{-4}\normalsize =-5.92[/latex]

[latex]\Large\frac{r}{-1.2}\normalsize =-6[/latex]

r = 7.2

[latex]\Large\frac{s}{-1.5}\normalsize =-3[/latex]

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

[latex]x - 5=-11[/latex]

x = −6

[latex]-\Large\frac{2}{5}\normalsize =x+\Large\frac{3}{4}[/latex]

[latex]p+8=-2[/latex]

p = −10

[latex]p+\Large\frac{2}{3}\normalsize =\Large\frac{1}{12}[/latex]

[latex]-4.2m=-33.6[/latex]

m = 8

[latex]q+9.5=-14[/latex]

[latex]q+\Large\frac{5}{6}\normalsize =\Large\frac{1}{12}[/latex]

[latex]q=-\Large\frac{3}{4}[/latex]

[latex]\Large\frac{8.6}{15}\normalsize =-d[/latex]

[latex]\Large\frac{7}{8}\normalsize m=\Large\frac{1}{10}[/latex]

[latex]m=\Large\frac{4}{35}[/latex]

[latex]\Large\frac{j}{-6.2}\normalsize =-3[/latex]

[latex]-\Large\frac{2}{3}\normalsize =y+\Large\frac{3}{8}[/latex]

[latex]y=-\Large\frac{25}{24}[/latex]

[latex]s - 1.75=-3.2[/latex]

[latex]\Large\frac{11}{20}\normalsize =-f[/latex]

[latex]f=-\Large\frac{11}{20}[/latex]

[latex]-3.6b=2.52[/latex]

[latex]-4.2a=3.36[/latex]

a = −0.8

[latex]-9.1n=-63.7[/latex]

[latex]r - 1.25=-2.7[/latex]

r = −1.45

[latex]\Large\frac{1}{4}\normalsize n=\Large\frac{7}{10}[/latex]

[latex]\Large\frac{h}{-3}\normalsize =-8[/latex]

h = 24

[latex]y - 7.82=-16[/latex]

Translate to an Equation and Solve

In the following exercises, translate and solve.

The difference of [latex]n[/latex] and [latex]1.9[/latex] is [latex]3.4[/latex].

[latex]n - 1.9=3.4;5.3[/latex]

The difference [latex]n[/latex] and [latex]1.5[/latex] is [latex]0.8[/latex].

The product of [latex]-6.2[/latex] and [latex]x[/latex] is [latex]-4.96[/latex].

−6.2x = −4.96; 0.8

The product of [latex]-4.6[/latex] and [latex]x[/latex] is [latex]-3.22[/latex].

The quotient of [latex]y[/latex] and [latex]-1.7[/latex] is [latex]-5[/latex].

[latex]\Large\frac{y}{-1.7}\normalsize =-5;8.5[/latex]

The quotient of [latex]z[/latex] and [latex]-3.6[/latex] is [latex]3[/latex].

The sum of [latex]n[/latex] and [latex]-7.3[/latex] is [latex]2.4[/latex].

n + (−7.3) = 2.4; 9.7

The sum of [latex]n[/latex] and [latex]-5.1[/latex] is [latex]3.8[/latex].