Question
Solve : $\frac{2}{3} \mathrm{x}+8<12 ; \mathrm{x} \in \mathrm{W}$
✓
Answer
$ \frac{2}{3} \mathrm{x}+8<12$
$ \Rightarrow \frac{2}{3} \mathrm{x}+8-8<12-8$
$ \Rightarrow \frac{2}{3} \mathrm{x}<4$
$ \Rightarrow \frac{2}{3} \mathrm{x} \times \frac{3}{2}<4 \times \frac{3}{2} ($Multiplying by $\frac{3}{2} \text { ) }$
$ \Rightarrow \mathrm{x}<6$
$ \therefore$ Required answer $=\{0,1,2,3,4,5\}$
$ \Rightarrow \frac{2}{3} \mathrm{x}+8-8<12-8$
$ \Rightarrow \frac{2}{3} \mathrm{x}<4$
$ \Rightarrow \frac{2}{3} \mathrm{x} \times \frac{3}{2}<4 \times \frac{3}{2} ($Multiplying by $\frac{3}{2} \text { ) }$
$ \Rightarrow \mathrm{x}<6$
$ \therefore$ Required answer $=\{0,1,2,3,4,5\}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In what time will the interest on a certain sum of money at $6 \%$ be $\frac{5}{8}$ of itself?
→Divide $x^6 – y^6$ by the product of $x^2 + xy + y^2$ and $x – y.$
→Verify Euler$\ ’$s formula for the following three$-$dimensional figures:
→A wall $9\ m$ long, $6\ m$ high and $20\ cm$ thick, is to be constructed using bricks of dimensions $30\ cm, 15\ cm$, and $10\ cm$. How many bricks will be required?
→Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :$8 − 3x, xy^2, 3y^2 − 5y + 8, 9x − 3x^2 + 15x^3 − 7,3x \times 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7$ and $4 − ax^2 + bx + y$
→Use the following figure to find the value of $x$
→Solve and graph the solution set on a number line : $ 8x – 8 \leq – 24 ; x \in Z$
→In rhombus $ABCD; (i)$ if $\angle A = 74^\circ$ ; find $\angle B$ and $\angle C.(ii)$ if $AD = 7.5 \ cm $; find $BC$ and $CD.$
→When the rate of sale$-$tax is decreased from $9\%$ to $6\%$ for a coloured $T.V$.; Mrs. Geeta will save $Rs \ 780$ in buying this $T.V$. Find the list price of the $T.V.$
→Solve : $15 – 2(2x – 1) < 15, x \in Z.$
→