Solve the equation for x: 3(10x + 12) - 3(42 + 22x) = -18136.
Understand the Problem
The question involves solving a mathematical equation for variable x. The steps leading to the equation and calculations are displayed, and the goal is to obtain the final value for x from the provided expressions.
Answer
$x \approx 501.28$
Answer for screen readers
The final answer is: $$ x \approx 501.28 $$
Steps to Solve
- Distribute the terms inside the parentheses
Start by distributing the 3 into both sets of parentheses: $$ 3(10x + 12) - 3(42 + 22x) = 30x + 36 - (126 + 66x) $$
- Combine like terms
Rearranging the equation: $$ 30x + 36 - 126 - 66x = -18136 $$ Combine the constants and the variable terms: $$ (30x - 66x) + (36 - 126) = -18136 $$ This simplifies to: $$ -36x - 90 = -18136 $$
- Isolate the variable x
Add 90 to both sides to isolate the term with x: $$ -36x = -18136 + 90 $$ Calculate: $$ -36x = -18046 $$
- Solve for x
Divide both sides by -36: $$ x = \frac{-18046}{-36} $$ This simplifies to: $$ x = \frac{18046}{36} $$ Now perform the division: $$ x = 501.28 $$
The final answer is: $$ x \approx 501.28 $$
More Information
The problem involves linear equations and the steps are fundamental in solving for a variable. It helps reinforce algebraic techniques such as distribution, combining like terms, and isolating variables.
Tips
- Forgetting to distribute the negative sign when subtracting terms.
- Not combining like terms correctly, which can lead to an incorrect equation.
- Miscalculating during division or the summation of constants.
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