Solving Linear Equations and Inequalities

Solve the equation $10x+14=2x+38$ explaining all the steps of your solution as in the examples in this section. 

In the following exercise, solve each linear equation. 

$8\left(22+11r\right)=0$

In the following exercise, solve each linear equation. 

$3\left(4n-1\right)-2=8n+3$

In the following exercise, solve each linear equation. 

$4\left(u-1\right)-8=6\left(3u-2\right)-7$

$Is y = \frac{4}{3} a solution of 9y + 2 = 6y + 3 ?$

$Is y = \frac{7}{5} a solution of 5y + 3 = 10y - 4 ?$

$\text{Solve: }x+19=-27$

$Solve: x + 16 = -34 .$

$\text{Solve}:n-61=-75.$

$Solve: p - 41 = -73.$

$\text{Solve: }p-\frac{2}{3}=\frac{5}{6}$

$\text{Solve:}q-\frac{1}{2}=\frac{5}{6}.$

$\text{Solve: }b-0.47=-2.1$

$\text{Solve: }c-0.93=-\mathrm{4.6.}$

$\text{Solve: }8y-4-7y-7=4$

$\text{Solve: }6z+5-5z-4=3.$

$\text{Solve: }5\left(p-3\right)-4p=-10.$

$\text{Solve: }4\left(q+2\right)-3q=-8.$

$\text{Solve: }4\left(2h-3\right)-7h=6\left(h-2\right)-6\left(h-1\right).$

$\text{Solve: }2\left(5x+2\right)-9x=3\left(x-2\right)-3\left(x-4\right).$

$\text{Translate and solve}:\text{ Ten more than x is equal to 41.}$

$\text{Translate and solve}:\text{Twelve less than x is equal to 51. }$

$\text{Translate and solve}:\text{The difference of 4x and 3x is 14}.$

$\text{Translate and solve}:\text{The difference of 7a and 6a is -8}.$

Translate into an algebraic equation and solve: The Pappas family has two cats, Zeus and Athena. Together, they weigh 23 pounds. Zeus weighs 16 pounds. How much does Athena weigh? 

Translate into an algebraic equation and solve: Sam and Henry are roommates. Together, they have 68 books. Sam has 26 books. How many books does Henry have?

Translate into an algebraic equation and solve: Eddie paid \(19,875 for his new car. This was \)1,025 less than the sticker price. What was the sticker price of the car? 

Translate into an algebraic equation and solve: 

The admission price for the movies during the day is \(7.75. This is \)3.25 less the price at night. How much does the movie cost at night? 

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

$\text{Is }y=\frac{5}{3}\text{ a solution of }6y+10=12y?$

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

$\text{Is x}=\frac{9}{4}\text{ a solution of 4x}+9=8x?$

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

$\text{Is u}=-\frac{1}{2}\text{ a solution of 8u-1}=6u?$ 

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

$\text{Is v}=-\frac{1}{3}\text{ a solution of 9v-2}=3v?$

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

$x+24=35$

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

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$y+45=-66$

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

$y+39=-83$ 

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$b+\frac{1}{4}=\frac{3}{4}$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$a+\frac{2}{5}=\frac{4}{5}$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$p+2.4=-9.3$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$m+7.9=11.6$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$a-45=76$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$a-30=57$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$m-18=-200$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$m-12=-12$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$x-\frac{1}{3}=2$

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

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$y-3.8=10$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$y-7.2=5$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$x-165=-420$

In the following exercise, solve each equation using the Subtraction and Addition Properties of Equality. 
$z-101=-314$