Question

name
1-4 lesson quiz
solving inequalities in one variable

1. which number line shows the solution to the inequality (-2(x - 1)>8)?

(options with number lines omitted)

1. tina is playing a computer game. she starts with 100 points, and she loses points based on these rules:

• each time a player passes a level: 8 points are lost.
• each time a player catches a flower, 3 points are lost.

part a
suppose tina catches 6 flowers per level. which inequality determines the number of levels, ( p ), that tina must pass to have fewer than 20 points left?
a ( 100 - 8p - 6p - 3pleq20 )
b ( 100 - 8p - 6p - 3p<20 )
c ( 100 - 8p - 6p\times3pleq20 )
d ( 100 - 8p-(3\times6)p<20 )
part b
tina must complete at least (square) levels.

1. graph the solution of the inequality (-3(x + 1)geq6) on the number line.

(options with number lines omitted)

1. which graph shows the solution of the inequality ( 2x-(3 - x)>x + 1 )?

(options with number lines omitted)

1. a video streaming company offers two monthly plans.

plan a: $3 per video viewed, plus a flat rate of $8 per month.
plan b: $5 per video viewed and no additional flat rate.
write an inequality to find when the cost of viewing ( n ) videos with plan a is less than with plan b.
(options for inequality building and solution omitted)
plan a is less expensive when
(options for ( n ) range omitted)
envision® florida b.e.s.t. algebra 1 • assessment resources

Explanation:

1.

Step1: Solve the inequality

First, expand and isolate $x$:
$-2(3x - 1) > 8$
$-6x + 2 > 8$
$-6x > 8 - 2$
$-6x > 6$
Divide by $-6$ (reverse inequality):
$x < -1$

Step2: Match to number line

The number line has an open circle at $-1$, shading left.

Step1: Define total lost points

Points lost: $8p$ (levels) + $3\times6p$ (flowers, 6 per level)

Step2: Set up inequality

Remaining points: $100 - 8p - 18p > 20$ → $100 - 8p - 6p\times3 < 20$

Step1: Simplify the inequality

$100 - 26p > 20$
$-26p > -80$
$p < \frac{80}{26} \approx 3.07$

Step2: Find minimum integer level

At least 1 level (since $p$ is positive integer, smallest is 1)

Answer:

$\boldsymbol{\text{Option C}}$

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2. Part A