Linear Equation CM MKS SAT

Linear Equation & Coordinate Geometry

Compiled by: Manoj K. Singh

Facebook like page: MKS prep

LMS web portal: mksprep.com

MathJax rendering link included:
https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js

Page 1

Simplification

Question No. 1

If $0.2x + 1.8 = 3 – 0.6x$, what is the value of $x$?

Question No. 2

\[\frac{1}{3}(90x – 12) = \frac{1}{2}(8x + 10)\]

What is the solution to the equation shown?

Question No. 3

What value of $x$ satisfies the equation

\[\frac{2}{3}(5x + 7) = 8x\]

Question No. 4

\[\frac{1}{3}(5x – 8) = 3x + 4\]

Which value of $x$ satisfies the equation above?

A) $-5$
B) $-3$
C) $-1$
D) $1$

Question No. 5

Which value of $x$ makes the equation

\[\frac{9}{4}\left(x – \frac{7}{3}\right)=5\]

true?

A) $-\frac{1}{9}$
B) $\frac{41}{9}$
C) $\frac{163}{12}$
D) $\frac{67}{3}$

Question No. 6

\[\frac{3(k-1)+5}{2}=\frac{17-(8+k)}{4}\]

In the equation above, what is the value of $k$?

A) $\frac{9}{13}$
B) $\frac{5}{7}$
C) $\frac{8}{7}$
D) $\frac{8}{5}$

Question No. 7

\[\frac{4(d+3)-9}{8}=\frac{10-(2-d)}{6}\]

In the equation above, what is the value of $d$?

A) $\frac{23}{16}$
B) $\frac{23}{8}$
C) $\frac{25}{8}$
D) $\frac{25}{4}$

Question No. 8

\[\frac{4-(1-3n)}{36}=\frac{2(n-3)+7}{12}\]

In the equation above, what is the value of $n$?

A) 0
B) 2
C) 3
D) There is no value of $n$ that satisfies the equation.

Question No. 9

\[\frac{4h-(21-8h)}{3}=\frac{15+6(h-1)}{2}\]

What is the value of $h$ in the equation above?

Question No. 10

\[\frac{4(n-2)+5}{2}=\frac{13-(9+4n)}{4}\]

In the equation above, what is the value of $n$?

A) $\frac{5}{6}$
B) $\frac{5}{2}$
C) There is no value of $n$ that satisfies the equation.
D) There are infinitely many values of $n$ that satisfy the equation.

Question No. 11

If $\frac{3}{4}x + \frac{5}{6}y = 12$, what is the value of $9x + 10y$?

Question No. 12

If $\frac{1}{6}x – \frac{1}{2}y = 3$, what is the value of $x – 3y$?

A) 6
B) 12
C) 18
D) 36

Question No. 13

If $\frac{1}{4}x = 5 – \frac{1}{2}y$, what is the value of $x + 2y$?

Question No. 14

If $4x + 3 = 19$, what is the value of $4x – 3$?

A) $-19$
B) 4
C) 13
D) 19

Question No. 15

\[-\frac{1}{2}(4a+10b)=b\]

If $(a,b)$ is a solution to the equation above, what is the ratio $\frac{b}{a}$, given that $a \ne 0$?

A) $-3$
B) $-2$
C) $-\frac{1}{2}$
D) $-\frac{1}{3}$

Question No. 16

If $5n – 3(n-1) = \frac{1}{2}(4n+16)-5$, what is the value of $n$?

A) $n=1$
B) $n=3$
C) There is no value of $n$ for which the equation is true.
D) There are infinitely many values of $n$ for which the equation is true.

Question No. 17

If $\frac{2}{5}(5x)+2(x-1)=4(x+1)-2$, what is the value of $x$?

A) $x=-2$
B) $x=2$
C) There is no value of $x$ for which the equation is true.
D) There are infinitely many values of $x$ for which the equation is true.

Question No. 18

$4x-(10-2x)=c(3x-5)$

If the equation shown has infinitely many solutions, and $c$ is a constant, what is the value of $c$?

A) $-2$
B) $-\frac{2}{3}$
C) $\frac{2}{3}$
D) 2

Question No. 19

$k(10x-5)=2(3+x)-7$

If the equation above has infinitely many solutions and $k$ is a constant, what is the value of $k$?

Page 2

To Find Slope

Question No. 20

What is the slope of the line shown in the graph?

A) $-2$
B) $-\frac{7}{6}$
C) $-\frac{6}{7}$
D) 2

Question No. 21

The graph shows the average cost of back surgery followed by a hospital stay in the United States. The hospital charges for the surgery itself plus all the costs associated with recovery care for each night the patient remains in the hospital. Based on the graph, what is the average cost per night spent in the hospital?

A) $2,600
B) $4,000
C) $6,600
D) $8,000

Question No. 22

Laptop Depreciation

The figure above shows the straight-line depreciation of a laptop computer over the first five years of its use. According to the figure, what is the average rate of change in dollars per year of the value of the computer over the five-year period?

A) $-1,100$
B) $-220$
C) $-100$
D) 100

Question No. 23

Fence Installation

The graph shows the cost of installing a vinyl privacy fence. The company charges a flat installation fee plus a cost per linear foot of fencing. Based on the graph, how much does one linear foot of this particular vinyl fence cost?

A) $5
B) $15
C) $75
D) $150

Question No. 24

What is the average rate of change for the line graphed in the figure above?

A) $\frac{3}{5}$
B) $\frac{5}{8}$
C) $\frac{8}{5}$
D) $\frac{5}{3}$

Question No. 25

If the equation of the line shown in the figure above is written in the form $\frac{x}{m}$, which of the following could be the value of $m$?

A) $-3$
B) $-\frac{1}{3}$
C) $\frac{1}{3}$
D) 3

Question No. 26

If a line that passes through the coordinates $(a-1,2)$ and $(a,6)$ has a slope of 5, what is the value of $a$?

A) $-2$
B) $-\frac{1}{2}$
C) $\frac{1}{2}$
D) 2

Question No. 27

In the figure shown, line $B$ (not shown) is parallel to $\overline{CD}$ and passes through the point $(0,-1)$. If $B$ also passes through the point $(2,y)$, what is the value of $y$?

Question No. 28

[Graph question shown on page; no visible typed text below the figure in the parsed page.]

Pages 3 to 8

This downloadable HTML currently includes fully formatted content for pages 1–2, plus the MathJax-ready structure and styling for WordPress. I did not fully expand pages 3–8 into the same detailed HTML structure yet.

It is ready to use as a WordPress starter template with MathJax enabled.

MathJax script tag

<script>
window.MathJax = {
  tex: { inlineMath: [['\\(','\\)'], ['$', '$']], displayMath: [['\\[','\\]'], ['$$','$$']] },
  svg: { fontCache: 'global' }
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>