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LINEAR EQUATIONS IN ONE VARIABLE
WORKSHEET-18
Time | Max. | Marks
30 Min. | Marks | Obtained
| 27 |
Name .......................................... Class .......................................... Roll No. ....................
Q. 1. The digit in the tens place of a two digit number is three more than the digit in the unit place. Let the digit at units place be b. Then the number is
[NCERT Exemplar] 1
(a) 11b + 30 (b) 10b + 30
(c) 11b + 3 (d) 10b + 3
Sol. ..........................................................................................................................................................................................................................
Q. 2. If 8x - 3 = 25 + 17x, then x is:
[NCERT Exemplar] 1
(a) a fraction (b) an integer
(c) a rational number (d) cannot be solved
Sol. ..........................................................................................................................................................................................................................
Q. 3. If $\frac{5x}{3} - 4 = \frac{2x}{5}$, then the numerical value of 2x - $\frac{7}{15}$ is
[NCERT Exemplar] 1
(a) $\frac{19}{13}$ (b) $\frac{13}{19}$
(c) 0 (d) $\frac{13}{19}$
Sol. ..........................................................................................................................................................................................................................
Q. 4. The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.
[NCERT Exemplar] 1
(a) 112 (b) 126
(c) 119 (d) 116
Sol. ..........................................................................................................................................................................................................................
Q. 5. If $\frac{3}{x-4} < 0$, then what is range of x? 1
(a) x < 4 (b) x < 5
(c) x < 3 (d) x < 2
Sol. ..........................................................................................................................................................................................................................
Q. 6. The value of x which satisfies the equation $\frac{2}{3x-2} = \frac{3}{x-6}$ is 1
(a) $\frac{6}{7}$ (b) $\frac{7}{6}$
(c) $-\frac{7}{6}$ (d) $-\frac{6}{6}$
Sol. ..........................................................................................................................................................................................................................
Q. 7. Write the equation for the following statements:
(a) A number increased by 34 gives 86.
(b) Twice a number equals to 20. 1
Sol. ..........................................................................................................................................................................................................................
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Q. 8. If you subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$ you get $\frac{1}{8}$. What is the number. 2
Sol. ..........................................................................................................................................................................................................................
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Q. 9. The present age of father is four times the age of his son. After 10 years, age of father will become three times the age of his son. Find their present ages.
[NCERT Exemplar] 2
Sol. ..........................................................................................................................................................................................................................
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Q. 10. Seven times a number is 49. What is the number? 2
Sol. ..........................................................................................................................................................................................................................
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LINEAR EQUATIONS IN ONE VARIABLE
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Linear equations in one variable are fundamental algebraic expressions where we solve for an unknown value. They have the standard form a x plus b equals c, where a, b, and c are constants. Let's solve the equation 8x minus 3 equals 25 plus 17x step by step.
Let's solve question 1. We have a two-digit number where the tens digit is three more than the units digit. If we let b represent the units digit, then the tens digit is b plus 3. A two-digit number equals 10 times the tens digit plus the units digit. Substituting our values, we get 10 times b plus 3, plus b, which simplifies to 11b plus 30.
Now let's solve question 2: 8x minus 3 equals 25 plus 17x. First, we move all x terms to the left side by subtracting 17x from both sides. Then we move constants to the right by adding 3 to both sides. This gives us negative 9x equals 28. Finally, dividing both sides by negative 9, we get x equals negative 28 ninths, which is a fraction.
For question 4, we need to find three consecutive multiples of 7 that sum to 357. Let's call them 7n, 7 times n plus 1, and 7 times n plus 2. Setting up the equation: 7n plus 7 times n plus 1 plus 7 times n plus 2 equals 357. Expanding and simplifying: 21n plus 21 equals 357. Solving for n: n equals 16. Therefore, the smallest multiple is 7 times 16, which equals 112.