If 4x - 28 = -24, what is the value of x - 7?
Understand the Problem
The question is asking to solve the equation 4x - 28 = -24 for the value of x and then to determine what x - 7 equals. This involves basic algebraic manipulation to isolate x and then substitute into the expression for x - 7.
Answer
The value of $x - 7$ is $-6$.
Answer for screen readers
The value of $x - 7$ is $-6$.
Steps to Solve
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Isolate the term with x To solve for $x$, we need to isolate the term with $x$ in the equation. Start with the original equation: $$4x - 28 = -24$$ Add 28 to both sides: $$4x - 28 + 28 = -24 + 28$$ This simplifies to: $$4x = 4$$
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Solve for x Now, divide both sides by 4 to find the value of $x$: $$x = \frac{4}{4}$$ This results in: $$x = 1$$
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Calculate x - 7 Now that we have the value of $x$, we can find $x - 7$: $$x - 7 = 1 - 7$$ This simplifies to: $$x - 7 = -6$$
The value of $x - 7$ is $-6$.
More Information
The solution shows that when you isolate the variable and perform basic algebraic operations, you can derive the value of expressions depending on that variable. Here, $x=1$ led us directly to the answer for $x-7$.
Tips
Common mistakes include:
- Forgetting to combine like terms correctly when isolating $x$.
- Not performing the operations in the correct order, especially with addition and subtraction.
