{4x+3<2x+5 {6x-7≤7x+2

To solve the two inequalities given, let’s break them down one at a time. ### Inequality 1: \[ 4x + 3 < 2x + 5 \] **Step 1**: Subtract \(2x\) from both sides: \[ 4x - 2x + 3 < 5 \] \[ 2x + 3 < 5 \] **Step 2**: Subtract \(3\) from both sides: \[ 2x < 5 - 3 \] \[ 2x < 2 \] **Step 3**: Divide by \(2\): \[ x < 1 \] ### Inequality 2: \[ 6x - 7 \leq 7x + 2 \] **Step 1**: Subtract \(6x\) from both sides: \[ -7 \leq 7x - 6x + 2 \] \[ -7 \leq x + 2 \] **Step 2**: Subtract \(2\) from both sides: \[ -7 - 2 \leq x \] \[ -9 \leq x \] or equivalently \( x \geq -9 \) ### Solution Summary: 1. From the first inequality, we have: \( x < 1 \) 2. From the second inequality, we have: \( x \geq -9 \) ### Combined Solution: The solution to the compound inequalities is: \[ -9 \leq x < 1 \] This means that \(x\) can take any value greater than or equal to \(-9\) but less than \(1\).