Bill is solving the equation 26x−21(6x+51)=40(11x+139). The following shows the steps he has used so far to solve the equation.
Step1:26x−21(6x)−21(51)=40(11x)+40(139)
Step2:26x−126x−1071=440x+5560
Which statement describes a possible next step that Bill can use to solve this equation?
Add 1071 to both sides of the equation. This will simplify the equation to 26x−126x=440x+6631.
Subtract 126x from both sides of the equation. The equation then becomes 26x−1071=313x+5560.
Subtract 440 from both sides of the equation. The equation now becomes 26x−126x−1511=0x+5560.
Add 5560. The equation becomes 26x−126x−4489=440x.
Add 1071 to both sides
26x -126x -1071 = 440x + 5560
-100x -1071 = 440x + 5560
-100x + 100x - 1071 = 100x + 440x + 5560
-1071 = 540x + 5560
-1071-5560 = 540x +5560-5560
-6631 = 540x
x = -6631/540
To help Bill solve the equation 26x−21(6x+51)=40(11x+139), let's go through the given steps first:
Step 1: Distribute (multiply) -21 to both terms inside the parentheses, and distribute 40 to both terms inside the other parentheses:
26x − 126x − 1071 = 440x + 5560
Step 2: Combine like terms on both sides of the equation:
−100x − 1071 = 440x + 5560
Now, let's analyze the answer choices and determine the possible next step:
1. Add 1071 to both sides of the equation. This will simplify the equation to:
−100x = 440x + 6631
This is not a correct next step since we need to simplify the equation, not further complicate it with additional terms.
2. Subtract 126x from both sides of the equation. The equation then becomes:
−226x − 1071 = 313x + 5560
This is also not a correct next step as it introduces unnecessary terms and does not simplify the equation.
3. Subtract 440 from both sides of the equation. The equation now becomes:
−100x − 1071 − 440 = 0x + 5560 - 440
Simplifying further:
−100x − 1511 = 0x + 5120
This is not a correct next step as it adds unnecessary terms and does not simplify the equation.
4. Add 5560. The equation becomes:
−100x − 1071 = 440x + 5560 + 5560
Simplifying further:
−100x − 1071 = 440x + 11120
This is the correct next step as it allows us to simplify the equation.
Therefore, the correct statement is:
Add 5560. The equation becomes 26x − 126x − 1071 = 440x + 11120.