1.4E: Exercises

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Aug 12, 2022
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- 1.4: Using Variables to Solve Equations
- 1.5: Solve Linear Inequalities

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Practice Makes Perfect

Verify a Solution

In the following exercises, determine whether the given value is a solution to the equation.

Is $y=\frac{5}{3}$ a solution of $6 y+10=12 y ?$
Is $u=-\frac{1}{2}$ a solution of $8 u-1=6 u ?$
Is $v=-\frac{1}{3}$ a solution of $9 v-2=3 v ?$
Is $v=\frac{1}{3}$ a solution of $9 v-2=3 v ?$

Answer

Solve Equations using Subtraction and Addition

In the following exercises, solve each equation using the Subtraction and Addition Properties of Equality.

$x+24=35$
$y+45=-66$
$b+\frac{1}{4}=\frac{3}{4}$
$p+2.4=-9.3$
$a-45=76$
$m-18=-200$
$x-\frac{1}{3}=2$
$y-3.8=10$
$x-165=-420$
$z+0.52=-8.5$
$q+\frac{3}{4}=\frac{1}{2}$
$p-\frac{2}{5}=\frac{2}{3}$
$c+31-10=46$
$9 x+5-8 x+14=20$
$-6 x-11+7 x-5=-16$

Answer

x = 11
y = -111
$b = \frac{1}{2}$
p = -11.7
a = 121
m = -182
$x=\frac{7}{3}$
y = 13.8
$x=-255$
$z=-9.02$
$q = -\frac{1}{4}$
$p=\frac{16}{15}$
c = 25
x = 1
x = 0

Solve Equations using Division and Multiplication

In the following exercises, solve each equation using the Division and Multiplication Properties of Equality.

$8x=56$
$-5 c=55$
$-809=15 y$
$-37 p=-541$
$0.25 z=3.25$
$-13x=0$
$\frac{x}{4} = 35$
$-20=\frac{q}{-5}$
$\frac{y}{9}=-16$
$\frac{m}{-12}=45$
$-y=6$
$-v=-72$
$-\frac{5}{8} w=40$
$-\frac{2}{5}=\frac{1}{10} a$
$100-16=4 p-10 p-p$
$\frac{7}{8} n-\frac{3}{4} n=9+2$
$0.25 d+0.10 d=6-0.75$
$-10(q-4)-57=93$
$-10(x+4)-19=85$

Answer

$x=7$
$c=-11$
$y = -\frac{809}{15}$
$p=\frac{541}{37}$
z= 13
$x=0$
$x=140$
$q=100$
$y=-144$
$m=-540$
$y=-6$
$v=72$
$w=-64$
$a=-4$
$p=-12$
$n=88$
d=15
$q=-11$
$x=-\frac{72}{5}$

Everyday Math

Construction Miguel wants to drill a hole for a $\frac{5}{8}$ inch screw. The hole should be $\frac{1}{12}$ inch smaller than the screw. Let $d$ equal the size of the hole he should drill. Solve the equation $d=\frac{5}{8}-\frac{1}{12}$ to see what size the hole should be.
Baking Kelsey needs $\frac{2}{3}$ cup of sugar for the cookie recipe she wants to make. She only has $\frac{3}{8}$ cup of sugar and will borrow the rest from her ner neighbor. Let $s$ equal the amount of sugar she will borrow. Solve the equation $\frac{3}{8}+s=\frac{2}{3}$ to find the amount of sugar she should ask to borrow.
Commissions Every week Perry gets paid $\$150$ plus 12% of his total sales amount. Solve the equation $840=150+0.12(a-1250)$ for $a$ to find the total amount Perry must sell in order to be paid $\$ 840$ one week.
Stamps Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s, to find the number of 49-cent stamps Travis bought.

Answer

$d=\frac{13}{24}$ inch
$s=\frac{7}{24}$ cups
$a=7000$
15 49-cent stamps

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Verify a Solution

Solve Equations using Subtraction and Addition

Solve Equations using Division and Multiplication

Everyday Math

Practice Makes Perfect

Verify a Solution

Solve Equations using Subtraction and Addition

Solve Equations using Division and Multiplication

Everyday Math

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