Home / Digital SAT Math – Linear equations in one variable – Practice Questions – Medium

Digital SAT Math – Linear equations in one variable – Practice Questions – Medium

Digital SAT Math - Linear equations in one variable - Practice Questions - Medium- New Syllabus

DSAT MAth Practice questions – all topics

  • Algebra Weightage: 35%  Questions: 13-15
    • Linear equations in one variable
    • Linear equations in two variables
    • Linear functions
    • Systems of two linear equations in two variables
    • Linear inequalities in one or two variables

▶️Last Minutes DSAT Math revision Sheet

▶️Desmos Calculator

DSAT MAth and English  – full syllabus practice tests

 Question  medium

\(3(2x-6)-11=4(x-3)+6\)

If x is the solution to the equation above, what is the value of \(x-3\)?

A \(\frac{23}{2}\)

B \(\frac{17}{2}\)

C \(\frac{15}{2}\)

D \(-\frac{15}{2}\)

▶️Answer/Explanation

Ans: B

To solve the equation 3(2x−6)−11=4(x−3)+6 using Desmos and find the value of x−3, follow these steps:

In the input bar, type the left side of the equation as a function: y=3(2x−6)−11
In the next input bar, type the right side as another function: y=4(x−3)+6
Desmos will graph both functions as lines.

x= 11.5
Hence \(x-3\) =11.5-3=8.5 =\(\frac{17}{2}\)
Question Medium

\[ 2x + 16 = a(x + 8) \]

In the given equation, \( a \) is a constant. If the equation has infinitely many solutions, what is the value of \( a \)?

A) 1

B) 2

C) 3

D) 8

▶️ Answer/Explanation
Solution

Ans: B

Expand: \( 2x + 16 = ax + 8a \)

Match coefficients: \( 2 = a \), \( 16 = 8a \)

Solve: \( a = \frac{16}{8} = 2 \)

Question Medium

\[ (b – 2)x = 8 \]

In the given equation, \( b \) is a constant. If the equation has no solution, what is the value of \( b \)?

A) 2

B) 4

C) 6

D) 10

▶️ Answer/Explanation
Solution

Ans: A

For no solution, \( b – 2 = 0 \), so \( b = 2 \)

Then \( 0 \cdot x = 8 \), a contradiction

Choice B: \( 2x = 8 \), has solution

Choice C: \( 4x = 8 \), has solution

Choice D: \( 8x = 8 \), has solution

Question Medium

An agricultural scientist studying the growth of corn plants recorded the height of a corn plant at the beginning of a study and the height of the plant each day for the next 12 days. The scientist found that the height of the plant increased by an average of 1.20 centimeters per day for the 12 days. If the height of the plant on the last day of the study was 36.8 centimeters, what was the height, in centimeters, of the corn plant at the beginning of the study?

A) 20.4

B) 22.4

C) 24.4

D) 51.2

▶️ Answer/Explanation
Solution

Ans: B

Total growth: \( 1.20 \times 12 = 14.4 \) cm

Initial height: \( 36.8 – 14.4 = 22.4 \) cm

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