Let's solve the inequalities step by step:

1. \(4x - 7 \leq 3x\)

Subtract \(3x\) from both sides:

\(x - 7 \leq 0\)

Add 7 to both sides:

\(x \leq 7\)

2. \(3x - 4 \leq 4x\)

Subtract \(3x\) from both sides:

\(-4 \leq x\)

Now we need to find the range of values of \(x\) that satisfy both inequalities. Since \(x\) must satisfy both \(x \leq 7\) and \(-4 \leq x\), the range of values for \(x\) is:

\(-4 \leq x \leq 7\)