Question

select all equations that have no solution. a. $4x - 10 - 2x = 2x - 3$ b. $12x - (6x + 3) = 7x$ c. $10 + 10x = 15 + 15x - 5x$ d. $12 + 21x - 7x = 8 + 14x$

Explanation:

Step1: Simplify left side of A

$4x-2x-10=2x-10$

Step2: Set equal to right side of A

$2x-10=2x-3$

Step3: Subtract $2x$ from both sides

$-10=-3$ (false, no solution)

Step4: Simplify and solve B

$12x-6x-3=7x \implies 6x-3=7x \implies x=-3$ (has solution)

Step5: Simplify and solve C

$10+10x=15+10x \implies 10=15$? No, wait: $15x-5x=10x$, so $10+10x=15+10x$ subtract $10x$: $10=15$? Correction: Wait no, re-simplify C: $10+10x=15+(15x-5x) \implies 10+10x=15+10x$, subtract $10x$: $10=15$ (false, no solution? Wait no, wait step 5 correction:

Step5: Simplify equation C

$10+10x=15+10x$

Step6: Subtract $10x$ from C

$10=15$ (false, no solution)

Step7: Simplify equation D

$12+14x=8+14x$

Step8: Subtract $14x$ from D

$12=8$ (false, no solution)
Wait correction, full recheck:

Step1: Solve Equation A

Simplify left: $4x-2x-10=2x-10$
Set equal to right: $2x-10=2x-3$
Subtract $2x$: $-10=-3$ → No solution

Step2: Solve Equation B

Simplify left: $12x-6x-3=6x-3$
Set equal to right: $6x-3=7x$
Solve: $x=-3$ → Has solution

Step3: Solve Equation C

Simplify right: $15+15x-5x=15+10x$
Set equal to left: $10+10x=15+10x$
Subtract $10x$: $10=15$ → No solution

Step4: Solve Equation D

Simplify left: $12+21x-7x=12+14x$
Set equal to right: $12+14x=8+14x$
Subtract $14x$: $12=8$ → No solution

Corrected Final Answer:
A. $4x - 10 - 2x = 2x - 3$, C. $10 + 10x = 15 + 15x - 5x$, D. $12 + 21x - 7x = 8 + 14x$

Answer:

A. $4x - 10 - 2x = 2x - 3$