Fill in the blanks to explain what needs to be done in the current step to get to the next step.
3x+4−2x+9=17−x
Step 1: 3x+4−2x+9=17−x
Step 2: x+13= 17−x
Step 3: x+x+13=17−x+x
Step 4: 2x +13 = 17
Step 5: 2x+13−13=17−13
Step 6: 2x=4
Step 7: x = 2
Step 1: The given equation is 3x+4−2x+9=17−x.
Step 2: Combine like terms on both sides of the equation. In this case, combine the x terms on the left side: 3x-2x = x. The right side remains the same: 17-x.
Step 3: Simplify both sides of the equation by adding or subtracting like terms. On the left side, add x to x+13 to get 2x+13. On the right side, combine -x and x to get 0. The equation becomes 2x+13=17.
Step 4: Isolate the variable term by subtracting 13 from both sides of the equation. This gives us 2x+13-13 = 17-13, which simplifies to 2x = 4.
Step 5: Simplify both sides further by performing the subtraction. On the left side, 13-13 equals 0, so the equation becomes 2x = 4.
Step 6: Solve for x by dividing both sides of the equation by 2. This gives us x = 4/2, which simplifies to x = 2.
Step 7: The final answer is x = 2.