Question

current learning objective: solving inequalities in one variable algebraically
question 20
score: 0 of 1 point
the following inequality has a solution in the form (x < a). solve the inequality and place the correct value of (a) into the box.
(4(x + 2)-1 < - 5x+1)
answer: (x <) enter your answer
note: enter your answer as an integer or a reduced fraction in the form (\frac{c}{b}).
submit answer attempts: 0/3
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Explanation:

Step1: Expand left - hand side

$4(x + 2)-1=4x+8 - 1=4x + 7$. So the inequality becomes $4x+7<-5x + 1$.

Step2: Add $5x$ to both sides

$4x+5x+7<-5x+5x + 1$, which simplifies to $9x+7<1$.

Step3: Subtract 7 from both sides

$9x+7 - 7<1 - 7$, resulting in $9x<-6$.

Step4: Divide both sides by 9

$x<-\frac{6}{9}=-\frac{2}{3}$.

Answer:

$x<-\frac{2}{3}$