Solving Equations and Inequalities

Identify the additive inverse for each number or expression.

$-3$

Identify the additive inverse for each number or expression. 

$2.5$

Identify the additive inverse for each number or expression.

$\frac{1}{4}$

Identify the additive inverse for each expression or expression.

$-3x$

Identify the additive inverse for each number or expression.

$5-6y$

Write a verbal expression to represent each equation.

$x-5=12$

Explain why the absolute value of a number is always nonnegative, $\left|a\right|$ can equal $-a$.

Write an absolute value equation for each solution set graphed below.

Determine whether the following statement is sometimes, always, or never true. Explain.

For all real numbers $a$and $b,a\ne 0$, the equation$\left|ax+b\right|=0$ will have one solution.

OPEN ENDED

Write and evaluate an expression with absolute value.

Evaluate each expression if $a=-4$  and b=1.5

$\left|a+12\right|$

Evaluate each expression if $a=-4$  and $b=1.5$ 

$\left|-6b\right|$

Evaluate each expression if $a=-4$  and $b=1.5$ 

$-\left|a+21\right|$ 

Solve each equation. Check your solution

$\left|x+4\right|=7$

Solve each equation. Check your solution

$\left|b+15\right|=3$

Solve each equation. Check your solution

$\left|a-9\right|=20$

Solve each equation. Check your solution

$\left|y-2\right|=34$

Solve each equation. Check your solution

$\left|2w+3\right|+6=2$

Solve each equation. Check your solution

$\left|c-2\right|=2c-10$

FOOD 

For exercise 14-16, use the following information.

A meat thermometer is used to assure that a safe temperature has been reached to destroy bacteria. Most meat thermometers are accurate to within plus or minus $2{}^{\circ }F$

The ham you are baking needs to reach an internal temperature of $160{}^{\circ }F$. If the thermometer reads $160{}^{\circ }F$, write an equation to determine the least and greatest temperature of the meat.

For exercise 14-16, use the following information.

A meat thermometer is used to assure that a safe temperature has been reached to destroy bacteria. Most meat thermometers are accurate to within plus or minus $2{}^{\circ }F$

Solve the equation you wrote in exercise 14

FOOD 

For exercise 14-16, use the following information.

A meat thermometer is used to assure that a safe temperature has been reached to destroy bacteria. Most meat thermometers are accurate to within plus or minus $2{}^{\circ }F$

16. To what temperature reading should you bake a ham to ensure that the minimum internal temperature is reached? Explain.

Evaluate each expression if a=-5,b=6 and c=2.8 

$\left|-3a\right|$ 

Evaluate each expression if a=-5, b=6  and c=2.8

$\left|-4b\right|$

Evaluate each expression if a=-5,b=6 and c=2.8

$\left|a+5\right|$

Evaluate each expression if a=-5,b=6   and c=2.8

$\left|2-b\right|$

Evaluate each expression if a=-5, b=6   and c=2.8

$\left|2b-15\right|$

Evaluate each expression if a=-5,b=6   and c=2.8

$\left|4a+7\right|$

Evaluate each expression if a=-5,b=6   and c=2.8

$-\left|18-5c\right|$

Evaluate each expression if a=-6, b=6  and c=2.8

$-\left|c-a\right|$

Evaluate each expression if a=-5,b=6   and c=2.8

$6-\left|3c+7\right|$ 

Evaluate each expression if a=-5, b=6   and c=2.8

$9-\left|-2b+8\right|$

Evaluate each expression if a=-5, b=6   and c=2.8

$3\left|a-10\right|+\left|2a\right|$ 

Evaluate each expression if a=-5,b=6   and c=2.8

$\left|a-b\right|-\left|10c-a\right|$

For the following statement, determine whether the statement is always, sometimes or never true. Explain your reasoning.

 If $a$and $b$real numbers, then $|a+b|=\left|a\right|+\left|b\right|$.

Solve each equation. Check your solution

$\left|x-25\right|=17$

Solve each equation. Check your solution

$\left|y+9\right|=21$ 

 Solve each equation. Check your solution

$\left|a+12\right|=33$

Solve each equation. Check your solution

$2\left|b+4\right|=48$ 

Solve each equation. Check your solution

 $8\left|w-7\right|=72$

Solve each equation. Check your solution

$\left|3x+5\right|=11$

Solve each equation. Check your solution

$\left|2z-3\right|=0$

Solve each equation. Check your solution

$\left|6c-1\right|=-2$ 

Solve each equation. Check your solution

$7\left|4x-13\right|=35$

Solve each equation. Check your solution

$-3\left|2n+5\right|=-9$

Solve each equation. Check your solution

$-12\left|9x+1\right|=144$

Solve the equation. Check the solutions.

$|5x+9|+6=1$

Solve the equation. Check the solutions.

$|a-3|-14=-6$

Solve the equation. Check the solutions.

$3|p-5|=2p$

Solve the equation. Check the solutions.

$3|2a+7|=3a+12$