Solve for all values of b in simplest form. |-5b+10|=40 Answer: b=

Split Absolute Value: We have the equation |-5b + 10| = 40. The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case.Positive Case: First, let's consider the positive case. We remove the absolute value bars and solve the equation: -5b + 10 = 40Positive Case Solution: Subtract 10 from both sides of the equation to isolate the term with b: -5b + 10 - 10 = 40 - 10 -5b = 30Negative Case: Now, divide both sides by -5 to solve for b: -5b / -5 = 30 / -5 b = -6Negative Case Solution: Next, let's consider the negative case. We remove the absolute value bars and solve the equation with a negative sign on the right side: -5b + 10 = -40Negative Case Solution: Subtract 10 from both sides of the equation to isolate the term with b: -5b + 10 - 10 = -40 - 10 -5b = -50Now, divide both sides by -5 to solve for b: -5b / -5 = -50 / -5 b = 10

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Solve for all values of
b in simplest form.

|-5b+10|=40
Answer:
b=

Solve for all values of $b$ in simplest form. $\newline$ $|-5 b+10|=40$ $\newline$ Answer: $b=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

b

in simplest form.

\newline

|-5 b+10|=40

\newline

Answer:

b=

Split Absolute Value: We have the equation $|-5b + 10| = 40$ . The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case.
Positive Case: First, let's consider the positive case. We remove the absolute value bars and solve the equation: $-5b + 10 = 40$
Positive Case Solution: Subtract $10$ from both sides of the equation to isolate the term with $b$ : $\newline$ $-5b + 10 - 10 = 40 - 10$ $\newline$ $-5b = 30$
Negative Case: Now, divide both sides by $-5$ to solve for $b$ : $\frac{-5b}{-5} = \frac{30}{-5}$ $b = -6$
Negative Case Solution: Next, let's consider the negative case. We remove the absolute value bars and solve the equation with a negative sign on the right side: $\newline$ $-5b + 10 = -40$
Negative Case Solution: Subtract $10$ from both sides of the equation to isolate the term with $b$ : $\newline$ $-5b + 10 - 10 = -40 - 10$ $\newline$ $-5b = -50$
Negative Case Solution: Subtract $10$ from both sides of the equation to isolate the term with $b$ : $\newline$ $-5b + 10 - 10 = -40 - 10$ $\newline$ $-5b = -50$ Now, divide both sides by $-5$ to solve for $b$ : $\newline$ $-5b / -5 = -50 / -5$ $\newline$ $b = 10$