Solving an Inequality
Sure, I'll help solve the inequality given in the image:
\((-3x + 7) + (-4x - 8) \geq -3x + 7\)
First, let's simplify the left side of the inequality by combining like terms:
\((-3x - 4x) + (7 - 8)\)
This simplifies to:
\(-7x - 1\)
Now, substitute this back into the inequality:
\(-7x - 1 \geq -3x + 7\)
To solve for \(x\), let's move all the terms with \(x\) on one side and the constant terms on the other side. First, add \(7x\) to both sides of the inequality:
\(-7x - 1 + 7x \geq -3x + 7 + 7x\)
This simplifies to:
\(-1 \geq 4x + 7\)
Next, subtract \(7\) from both sides:
\(-1 - 7 \geq 4x + 7 - 7\)
Which is:
\(-8 \geq 4x\)
Now, divide both sides by \(4\) to solve for \(x\):
\(-2 \geq x\), or equivalently written as \(x \leq -2\)
So the solution to the inequality is \(x \leq -2\).
