-5b+2(b-1) >= 6-(2b-1)+2b

Distribute 2: Distribute the 2 into the parentheses on the left side of the inequality. -5b + 2(b - 1) = -5b + 2b - 2Distribute negative sign: Distribute the negative sign into the parentheses on the right side of the inequality. 6 - (2b - 1) + 2b = 6 - 2b + 1 + 2bCombine like terms: Combine like terms on both sides of the inequality. Left side: -5b + 2b - 2 = -3b - 2 Right side: 6 - 2b + 1 + 2b = 7Write simplified inequality: Write the simplified inequality. -3b - 2 >= 7Add 2 to isolate: Add 2 to both sides of the inequality to isolate the term with the variable b. -3b - 2 + 2 >= 7 + 2 -3b >= 9Divide to solve for b: Divide both sides of the inequality by -3 to solve for b. Remember that dividing by a negative number reverses the inequality sign. -3b / -3 <= 9 / -3 b <= -3

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$-5 b+2(b-1) \geq 6-(2 b-1)+2 b$

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Math Problems

Grade 8

Solve multi-step equations with fractional coefficients

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-5 b+2(b-1) \geq 6-(2 b-1)+2 b

Distribute $2$ : Distribute the $2$ into the parentheses on the left side of the inequality. $-5b + 2(b - 1) = -5b + 2b - 2$
Distribute negative sign: Distribute the negative sign into the parentheses on the right side of the inequality. $\newline$ $6 - (2b - 1) + 2b = 6 - 2b + 1 + 2b$
Combine like terms: Combine like terms on both sides of the inequality. $\newline$ Left side: $-5b + 2b - 2 = -3b - 2$ $\newline$ Right side: $6 - 2b + 1 + 2b = 7$
Write simplified inequality: Write the simplified inequality. $\newline$ $-3b - 2 \geq 7$
Add $2$ to isolate: Add $2$ to both sides of the inequality to isolate the term with the variable $b$ . $-3b - 2 + 2 \geq 7 + 2$ $-3b \geq 9$
Divide to solve for b: Divide both sides of the inequality by $-3$ to solve for $b$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $-3b / -3 \leq 9 / -3$ $\newline$ $b \leq -3$