what is -3x + 7 = 19? PLEASE SHOW YOUR WORK
The Correct Answer and Explanation is:
To solve the equation:
−3x + 7 = 19
Step-by-Step Solution:
- Start with the original equation: −3x+7=19-3x + 7 = 19−3x+7=19
- Subtract 7 from both sides to isolate the term with the variable: −3x+7−7=19−7-3x + 7 – 7 = 19 – 7−3x+7−7=19−7 −3x=12-3x = 12−3x=12
- Divide both sides by −3 to solve for x: −3x−3=12−3\frac{-3x}{-3} = \frac{12}{-3}−3−3x=−312 x=−4x = -4x=−4
Final Answer:
x=−4x = -4x=−4
Explanation
To solve the linear equation −3x plus 7 equals 19, we need to isolate the variable x on one side of the equation. Linear equations like this one are equations where the variable has no exponents and the graph of the equation would be a straight line.
The first step is to eliminate the constant term on the left side of the equation. The constant is the number that is added to or subtracted from the variable term. In this case, the constant is plus 7. We eliminate it by performing the opposite operation, which is subtracting 7 from both sides of the equation. This keeps the equation balanced and does not change its truth value.
When we subtract 7 from both sides, we get −3x equals 12. Now the equation only contains the variable term on the left side.
The next step is to get x by itself. The coefficient of x is −3. To isolate x, we divide both sides of the equation by −3. Again, we do the same operation to both sides to keep the equation balanced.
After dividing both sides by −3, we get x equals −4.
To check our answer, we substitute x equals −4 back into the original equation. That means we replace x with −4 and evaluate:
−3 times −4 equals 12. Then 12 plus 7 equals 19, which matches the right-hand side of the equation.
Therefore, x equals −4 is the correct solution.
