Pregunta
Solve the inequality. \( 4<-5 x-6 \) i. The answer as an inequality is \[ x ? \hat{v} \text { (Enter oo for } \] ii. The answer in interval notation is \( \infty) \)
Ask by Phillips Cox. in the United States
Feb 27,2025
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\( x < -2 \)
\((- \infty, -2)\)
Solución
Solve the equation \( 4<-5x-6 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(4<-5x-6\)
- step1: Swap the sides:
\(-5x-6>4\)
- step2: Move the constant to the right side:
\(-5x>4+6\)
- step3: Add the numbers:
\(-5x>10\)
- step4: Change the signs:
\(5x<-10\)
- step5: Divide both sides:
\(\frac{5x}{5}<\frac{-10}{5}\)
- step6: Divide the numbers:
\(x<-2\)
The solution to the inequality \(4<-5x-6\) is \(x<-2\).
i. The answer as an inequality is \(x<-2\).
ii. The answer in interval notation is \((- \infty, -2)\).
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Simplifique esta solución The Deep Dive
To solve the inequality \( 4 < -5x - 6 \), first isolate \( x \). Start by adding 6 to both sides: \[ 4 + 6 < -5x \] This simplifies to: \[ 10 < -5x \] Next, divide both sides by -5. Remember to flip the inequality sign when dividing by a negative number: \[ \frac{10}{-5} > x \] So we have: \[ -2 > x \] or equivalently: \[ x < -2 \] i. The answer as an inequality is \[ x < -2 \] ii. The answer in interval notation is \( (-\infty, -2) \)
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