She added 4, multiplied the sum by -5, and subtracted 12. She then doubled the result and got -34. What number did Christa started with???
2[-5(x + 4) -12] = -34
Solve for x.
To determine the number Christa started with, we need to work backward from the final result. Let's break down the problem step by step:
1. "She added 4." Let's denote the unknown number as x. After adding 4, the result is x + 4.
2. "Multiplied the sum by -5." Multiply (x + 4) by -5: -5(x + 4) = -5x - 20.
3. "Subtracted 12." Subtract 12 from the previous result: -5x - 20 - 12 = -5x - 32.
4. "Doubled the result." Double (-5x - 32): 2(-5x - 32) = -10x - 64.
5. "Got -34." Set the doubled result equal to -34: -10x - 64 = -34.
Now, let's solve the equation to find the value of x:
-10x - 64 = -34
First, let's isolate the variable by moving the constant terms (in this case, -64) to the right side:
-10x = -34 + 64
-10x = 30
Next, divide both sides of the equation by -10 to solve for x:
x = 30 / -10
x = -3
Therefore, the number Christa started with is -3.