For what values of \( x \) is the inequality \( 10+3 x>2(3+4 x)+5 \) true?

To solve the inequality \( 10 + 3x > 2(3 + 4x) + 5 \), we first simplify the right side. Start by distributing the 2 in the expression \( 2(3 + 4x) \): \[ 2(3 + 4x) = 6 + 8x \] Now, substitute this back into the inequality: \[ 10 + 3x > 6 + 8x + 5 \] Combine the constants on the right: \[ 10 + 3x > 11 + 8x \] Next, we need to get all the \( x \) terms on one side and the constants on the other. Subtract \( 3x \) and \( 11 \) from both sides: \[ 10 - 11 > 8x - 3x \] This simplifies to: \[ -1 > 5x \] Now, divide both sides by 5 (remember, when dividing by a positive number, the direction of the inequality stays the same): \[ -\frac{1}{5} > x \] This can also be written as: \[ x < -\frac{1}{5} \] Thus, the solution to the inequality \( 10 + 3 x > 2(3 + 4 x) + 5 \) is: \[ x < -\frac{1}{5} \]