o) \( -(2 x+7)

Ask by Chan Harper. in Chile

Nov 11,2024

To solve the inequality \( -(2x + 7) < x + 3 \), first distribute the negative sign: \( -2x - 7 < x + 3 \). Now, let's get all terms involving \( x \) on one side by adding \( 2x \) to both sides: \( -7 < 3x + 3 \). Next, isolate \( 3x \) by subtracting \( 3 \) from both sides: \( -10 < 3x \), or \( 3x > -10 \). Finally, divide by \( 3 \): \( x > -\frac{10}{3} \). So, the solution is \( x > -\frac{10}{3} \). As for a fun example, think of this as a race! You want to beat the -10/3 finish line, meaning you need to run your \( x \) value faster than that. So, while you're at it, keep your pace up and run higher than -3.33 on that number line! And if you’re curious about practical applications, inequalities are everywhere in real life. Imagine budgeting your money: if \( x \) represents your expenditures, you want your total spending to stay below what you can afford (which might be derived from this kind of inequality). This can help you manage finances better while having a bit of fun with numbers!