Question

when solving ( x - 9(x + 7) > 8 - 3x ), what is the goal?

• to have the variable ( x ) on one side of a statement, and the variable ( y ) on the other
• to have the variable ( x ) on one side of an inequality, and the constant on the other
• to have the variable ( x ) on one side of an equation, and the constant on the other
• to have the variable ( x ) on one side of an expression, and the constant on the other

question 2
1 point
complete the inequality after solving ( 11x - 7 - 5x < -271 - 5x ). (fill each blank with an integer or a variable.)
__ < __

question 3
1 point
complete the inequality after solving ( 7(6x - 1) - 3x > 2x + 294 - 5x - 7 ). (fill each blank with an integer or inequality symbol.)
x __ __

Explanation:

Question 1

The given problem is a linear inequality with variable $x$. The goal of solving such an inequality is to isolate the variable on one side and move all constant terms to the opposite side. We eliminate incorrect options: there is no $y$, it is an inequality not an equation/expression.

Step1: Simplify left side

$11x - 7 - 5x = 6x - 7$

Step2: Add $5x$ to both sides

$6x - 7 + 5x < -271 - 5x + 5x$
$11x - 7 < -271$

Step3: Isolate variable term

$11x < -271 + 7$
$11x < -264$

Step4: Solve for $x$

$x < \frac{-264}{11}$
$x < -24$

Step1: Expand left side

$7(6x - 1) = 42x - 7$
$42x - 7 - 3x = 39x - 7$

Step2: Simplify right side

$2x + 394 - 5x - 7 = -3x + 387$

Step3: Add $3x$ to both sides

$39x - 7 + 3x > -3x + 387 + 3x$
$42x - 7 > 387$

Step4: Isolate variable term

$42x > 387 + 7$
$42x > 394$

Step5: Solve for $x$

$x > \frac{394}{42}$
$x > \frac{197}{21}$ or $x > 9\frac{8}{21}$

Answer:

To have the variable x on one side of an inequality, and the constants on the other

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Question 2