Question - Solving an Inequality
Solution:
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 $$x \leq -2$$.
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