Solve for all values of a in simplest form. |a+21|=22 Answer: a=

Understand absolute value equation: Understand the absolute value equation |a+21|=22. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, |a+21|=22 means that the expression a+21 is 22 units away from zero on the number line. This can happen in two ways: either a+21 is 22 or a+21 is -22.Set up two equations: Set up two separate equations to solve for a. Since a+21 can be either 22 or -22, we write two equations: 1. a+21 = 22 2. a+21 = -22Solve first equation: Solve the first equation a+21 = 22. Subtract 21 from both sides of the equation to isolate a: a + 21 - 21 = 22 - 21 a = 1Solve second equation: Solve the second equation a+21 = -22. Subtract 21 from both sides of the equation to isolate a: a + 21 - 21 = -22 - 21 a = -43

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Solve for all values of
a in simplest form.

|a+21|=22
Answer:
a=

Solve for all values of $a$ in simplest form. $\newline$ $|a+21|=22$ $\newline$ Answer: $a=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

a

in simplest form.

\newline

|a+21|=22

\newline

Answer:

a=

Understand absolute value equation: Understand the absolute value equation $|a+21|=22$ . $\newline$ The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|a+21|=22$ means that the expression $a+21$ is $22$ units away from zero on the number line. This can happen in two ways: either $a+21 = 22$ or $a+21 = -22$ .
Set up two equations: Set up two separate equations to solve for $a$ . Since $a+21$ can be either $22$ or $-22$ , we write two equations: $\newline$ $1$ . $a+21 = 22$ $\newline$ $2$ . $a+21 = -22$
Solve first equation: Solve the first equation $a+21 = 22$ . Subtract $21$ from both sides of the equation to isolate $a$ : $a + 21 - 21 = 22 - 21$ $a = 1$
Solve second equation: Solve the second equation $a+21 = -22$ . Subtract $21$ from both sides of the equation to isolate $a$ : $a + 21 - 21 = -22 - 21$ $a = -43$