Solve for all values of b in simplest form. 37=|5b+3| Answer: b=

Equation Explanation: We have the equation 37 = |5b + 3|. The absolute value equation means that the expression inside the absolute value, 5b + 3, can be either positive or negative, but its absolute value must be 37.Consider Absolute Value Cases: To solve the equation, we need to consider both cases for the absolute value: when 5b + 3 is positive and when it is negative. This gives us two separate equations to solve: 1. 5b + 3 = 37 2. 5b + 3 = -37Solve First Equation: Solve the first equation 5b + 3 = 37. Subtract 3 from both sides to isolate the term with b. 5b + 3 - 3 = 37 - 3 5b = 34 Now, divide both sides by 5 to solve for b. b = 34 / 5 b = 6.8Solve Second Equation: Solve the second equation 5b + 3 = -37. Subtract 3 from both sides to isolate the term with b. 5b + 3 - 3 = -37 - 3 5b = -40 Now, divide both sides by 5 to solve for b. b = -40 / 5 b = -8

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Solve for all values of
b in simplest form.

37=|5b+3|
Answer:
b=

Solve for all values of $b$ in simplest form. $\newline$ $37=|5 b+3|$ $\newline$ 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

37=|5 b+3|

\newline

Answer:

b=

Equation Explanation: We have the equation $37 = |5b + 3|$ . The absolute value equation means that the expression inside the absolute value, $5b + 3$ , can be either positive or negative, but its absolute value must be $37$ .
Consider Absolute Value Cases: To solve the equation, we need to consider both cases for the absolute value: when $5b + 3$ is positive and when it is negative. This gives us two separate equations to solve: $\newline$ $1$ . $5b + 3 = 37$ $\newline$ $2$ . $5b + 3 = -37$
Solve First Equation: Solve the first equation $5b + 3 = 37$ . $\newline$ Subtract $3$ from both sides to isolate the term with $b$ . $\newline$ $5b + 3 - 3 = 37 - 3$ $\newline$ $5b = 34$ $\newline$ Now, divide both sides by $5$ to solve for $b$ . $\newline$ $b = \frac{34}{5}$ $\newline$ $b = 6.8$
Solve Second Equation: Solve the second equation $5b + 3 = -37$ . Subtract $3$ from both sides to isolate the term with $b$ . $5b + 3 - 3 = -37 - 3$ $5b = -40$ Now, divide both sides by $5$ to solve for $b$ . $b = -40 / 5$ $b = -8$