Question

resolver $3(t + 1) - 4 \text{ toneladas} \geq -5$. grafique el conjunto solución en la recta numérica.

Explanation:

Step1: Simplify the left side

First, expand \( 3(t + 1) - 4 \). Using the distributive property, \( 3(t + 1)=3t + 3 \), so the inequality becomes \( 3t + 3 - 4 \geq -5 \). Then simplify \( 3 - 4=-1 \), so we have \( 3t - 1 \geq -5 \).

Step2: Isolate the variable term

Add 1 to both sides of the inequality: \( 3t - 1 + 1 \geq -5 + 1 \), which simplifies to \( 3t \geq -4 \).

Step3: Solve for t

Divide both sides by 3: \( t \geq \frac{-4}{3} \approx -1.33 \). Wait, there might be a translation error in the original problem (the "toneladas" seems out of place, maybe a typo). Assuming the inequality is \( 3(t + 1)-4 \geq -5 \) (ignoring the incorrect unit), let's re - solve:

Start over: \( 3(t + 1)-4\geq - 5\)

Expand: \(3t+3 - 4\geq - 5\)

Simplify: \(3t - 1\geq - 5\)

Add 1 to both sides: \(3t\geq - 5 + 1= - 4\)

Divide by 3: \(t\geq-\frac{4}{3}\approx - 1.33\)

But if we assume the original inequality was \(3(t + 1)-4\geq - 5\) with a possible typo and the number line in the image is a distraction or wrong, the solution for \(t\) is \(t\geq-\frac{4}{3}\). However, if we consider that maybe the inequality was \(3(t + 1)-4\leq - 5\) (to match the number line's left - oriented part), let's check:

\(3(t + 1)-4\leq - 5\)

\(3t+3 - 4\leq - 5\)

\(3t - 1\leq - 5\)

\(3t\leq - 4\)

\(t\leq-\frac{4}{3}\), but the number line in the image has a segment from around 3.5 to 4.5. Maybe the original inequality was \(3(t - 1)-4\geq - 5\) (correcting the sign in the parentheses):

\(3(t - 1)-4\geq - 5\)

\(3t-3 - 4\geq - 5\)

\(3t - 7\geq - 5\)

\(3t\geq2\)

\(t\geq\frac{2}{3}\approx0.67\), still not matching. Alternatively, if the inequality is \(3(t + 1)-4\leq5\):

\(3t + 3-4\leq5\)

\(3t - 1\leq5\)

\(3t\leq6\)

\(t\leq2\), no. Another approach: maybe the inequality is \(3(t + 1)-4\geq - 5\) and the number line in the image is incorrect. The correct solution for \(3(t + 1)-4\geq - 5\) is \(t\geq-\frac{4}{3}\).

But if we assume that the original problem was miswritten and the inequality is \(3(t + 1)-4\leq - 5\), the solution is \(t\leq-\frac{4}{3}\).

Since the number line in the image has a segment from a hollow circle (open dot) at around 3.5 to a solid dot at 4.5, let's assume the inequality is \(3(t + 1)-4\leq - 5\) is wrong. Let's try \(3(t - 3)-4\geq - 5\):

\(3t-9 - 4\geq - 5\)

\(3t - 13\geq - 5\)

\(3t\geq8\)

\(t\geq\frac{8}{3}\approx2.67\), no.

Alternatively, maybe the inequality is \(3(t + 1)-4\leq7\):

\(3t+3 - 4\leq7\)

\(3t - 1\leq7\)

\(3t\leq8\)

\(t\leq\frac{8}{3}\approx2.67\), no.

Wait, perhaps the original problem is \(3(t + 1)-4\geq - 5\) and the number line in the image is not related. The correct algebraic solution is:

1. Expand: \(3t + 3-4\geq - 5\)
2. Simplify: \(3t - 1\geq - 5\)
3. Add 1: \(3t\geq - 4\)
4. Divide by 3: \(t\geq-\frac{4}{3}\)

Answer:

The solution to the inequality \(3(t + 1)-4\geq - 5\) (assuming "toneladas" is a typo) is \(t\geq-\frac{4}{3}\) or approximately \(t\geq - 1.33\). If we consider the number line in the image as a mistake, and the inequality was intended to be solved algebraically, the solution is \(t\geq-\frac{4}{3}\).