What value of x makes the equation true? 2(x + 1) = -3x + 37
Understand the Problem
The question is asking for the value of x that satisfies the given equation. To solve this, we need to isolate x on one side of the equation.
Answer
The solution is \(x = 7\).
Answer for screen readers
The value of (x) that makes the equation true is (x = 7).
Steps to Solve
- Distribute the left side of the equation
Start by distributing the (2) in the equation: $$ 2(x + 1) = 2x + 2 $$ So the equation becomes: $$ 2x + 2 = -3x + 37 $$
- Combine like terms
Next, we can move the (3x) from the right side to the left by adding (3x) to both sides: $$ 2x + 3x + 2 = 37 $$ This simplifies to: $$ 5x + 2 = 37 $$
- Isolate the variable (x)
Now, subtract (2) from both sides to isolate the (5x): $$ 5x = 37 - 2 $$ This gives us: $$ 5x = 35 $$
- Solve for (x)
Finally, divide both sides by (5) to find (x): $$ x = \frac{35}{5} $$ Thus: $$ x = 7 $$
The value of (x) that makes the equation true is (x = 7).
More Information
In this equation, we used the distributive property and combined like terms to isolate (x). This method works for many linear equations.
Tips
- Forgetting to distribute properly when applying the distributive property.
- Failing to combine like terms consistently.
- Miscalculating when adding or subtracting on both sides of the equation.
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