What value of x makes the equation true? 5(5 - 3b) = -20 - 6b
Understand the Problem
The question is asking for the value of x that satisfies the given equation. This requires solving the equation through algebraic manipulation to isolate x.
Answer
The value of \( b \) is \( 5 \).
Answer for screen readers
The value of ( b ) that makes the equation true is ( b = 5 ).
Steps to Solve
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Distribute the Left Side Distribute the 5 on the left side of the equation: $$ 5(5 - 3b) = 25 - 15b $$ So the equation becomes: $$ 25 - 15b = -20 - 6b $$
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Rearrange the Equation Move the terms involving ( b ) to one side and the constant terms to the other side: $$ 25 + 20 = -6b + 15b $$ Which simplifies to: $$ 45 = 9b $$
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Isolate ( b ) To isolate ( b ), divide both sides by 9: $$ b = \frac{45}{9} $$ This simplifies to: $$ b = 5 $$
The value of ( b ) that makes the equation true is ( b = 5 ).
More Information
This calculation shows how to simplify and solve a linear equation through distribution and rearranging terms. The final value of ( b ) indicates that substituting ( 5 ) back into the equation will satisfy it.
Tips
- Forgetting to distribute correctly: Always ensure that every term inside the parentheses is multiplied by the factor outside.
- Mismanaging signs when moving terms: Be careful with positive and negative signs when rearranging the equation.
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