practice exercises

show all work. write complete sentences where required.

1. if $3(x-4)+2 = 5x-10$, find $x$.

2. a line through $(2,-3)$ is perpendicular to $y=(1/2)x+7$. find the equation of the line.

3. for what values of $x$ is $f(x) = x^2-4x+3$ less than zero?

Question

practice exercises

show all work. write complete sentences where required.

1. if $3(x-4)+2 = 5x-10$, find $x$.

2. a line through $(2,-3)$ is perpendicular to $y=(1/2)x+7$. find the equation of the line.

3. for what values of $x$ is $f(x) = x^2-4x+3$ less than zero?

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear Equation Solving", "Perpendicular Line Equations", "Quadratic Inequalities" ], "current_concepts": [ "Linear Equation Solving", "Perpendicular Line Equations", "Quadratic Inequalities" ] } ## Solve the linear equation for x $$ \begin{aligned} 3(x-4)+2 &= 5x-10 \ 3x-12+2 &= 5x-10 \ 3x-10 &= 5x-10 \ -10+10 &= 5x-3x \ 0 &= 2x \ x &= 0 \end{aligned} $$ ## Find the perpendicular line equation $$ \begin{aligned} m_1 &= \frac{1}{2} \implies m_2 = -2 \ y - y_1 &= m_2(x - x_1) \ y - (-3) &= -2(x - 2) \ y + 3 &= -2x + 4 \ y &= -2x + 1 \end{aligned} $$ ## Solve the quadratic inequality $$ \begin{aligned} x^2-4x+3 &< 0 \ (x-1)(x-3) &< 0 \ 1 &< x < 3 \end{aligned} $$ ## Question 1 $x = 0$ ## Question 2 $y = -2x + 1$ ## Question 3 $1 < x < 3$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Solve the linear equation for x

Find the perpendicular line equation

Solve the quadratic inequality

Answer:

Question 1

Question 2

Question 3