Math Snap

STEP 1

1. The equation $-2(5x - 3) + 8 = -10x + 14$ is a linear equation in one variable.
2. We need to simplify and solve for $x$.
3. The solution could be a specific value, all real numbers, or no solution.

STEP 2

1. Simplify both sides of the equation.
2. Collect like terms and isolate the variable $x$.
3. Determine the solution type based on the simplified equation.

STEP 3

Distribute the $-2$ on the left side of the equation:
$$-2(5x - 3) = -2 \cdot 5x + (-2) \cdot (-3) = -10x + 6$$ So the equation becomes:
$$-10x + 6 + 8 = -10x + 14$$

STEP 4

Combine the constant terms on the left side:
$$-10x + 14 = -10x + 14$$

STEP 5

Notice that both sides of the equation are identical:
$$-10x + 14 = -10x + 14$$ This implies that the equation is true for all values of $x$.

Since the equation is true for all values of $x$, the solution is:
B. The solution is all real numbers.