Ex.4.3 Q1 Simple-Equations Solutions-Ncert Maths Class 7

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Question

Solve the following equations.

(a) \(\begin{align} 2y + \frac{5}{2} = \frac{{37}}{2}\end{align} \)

(b)  \(\begin{align} 5t + 28 = 10\end{align} \)

(c) \(\begin{align} \frac{a}{5} + 3 = 2\end{align} \)

(d) \(\begin{align} \frac{q}{4} + 7 = 5\end{align} \)

(e) \(\begin{align} \frac{5}{2}x = - 5\end{align} \)

(f) \(\begin{align} \frac{5}{2}x = \frac{{25}}{4}\end{align} \)

(g) \(\begin{align} 7m + \frac{{19}}{2} = 13\end{align} \)

(h)  \(\begin{align} 6z + 10 = - 2\end{align} \)

(i) \(\begin{align} \frac{{3l}}{2} = \frac{2}{3}\end{align} \)

(j) \(\begin{align} \frac{{2b}}{3} - 5 = 3\end{align} \)

Text Solution

What is Known?

Equations.

What is unknown?

Solution of the equations (The value of the variable).

Reasoning:

To solve these equations, first transpose the variables on the one side and constants on the other side, then simplify them and get the value of variable.

Steps:

(a) \(\begin{align} 2y + \frac{5}{2} = \frac{{37}}{2}\end{align} \)

Transposing \(\begin{align} \frac{5}{2}\end{align} \) to R.H.S we get,

\[\begin{align}2y &= \frac{{37}}{2} - \frac{5}{2}\\2y &= \frac{{32}}{2} = 16\\y &= \frac{{16}}{2} = 8\end{align}\]

(b)  \(\begin{align} 5t + 28 = 10\end{align} \)

Transposing \(28\) to R.H.S we get,

\[\begin{align}5t &= 10 - 28\\5t &= - 18\\t &= \frac{{ - 18}}{5}\end{align}\]

(c) \(\begin{align} \frac{a}{5} + 3 = 2\end{align} \)

Transposing \(3\) to R.H.S we get,

\[\begin{align}\frac{a}{5} &= 2 - 3\\\frac{a}{5} &= - 1\\a &= - 5\end{align}\]

(d) \(\begin{align} \frac{q}{4} + 7 = 5\end{align} \)

Transposing \(7\) to R.H.S we get,

\[\begin{align}\frac{q}{4} &= 5 - 7\\\frac{q}{4} &= - 2\\q &= - 8\end{align}\]

(e) \(\begin{align} \frac{5}{2}x = - 5\end{align} \)

\[\begin{align}5x &= - 5 \times 2\\x &= \frac{{ - 10}}{5}\\x &= - 2\end{align}\]

(f) \(\begin{align} \frac{5}{2}x = \frac{{25}}{4}\end{align} \)

\[\begin{align}5x &= \frac{{25}}{4} \times 2\\x &= \frac{{25}}{{2 \times 5}}\\x &= \frac{5}{2}\end{align}\]

(g)  \(\begin{align} 7m + \frac{{19}}{2} = 13\end{align} \)

Transposing \(\begin{align} \frac{{19}}{2}\end{align} \) to the R.H.S.

\[\begin{align}7m&= 13 - \frac{{19}}{2}\\7m &= \frac{{26 - 19}}{2}\\7m &= \frac{7}{2}\\m &= \frac{7}{{2 \times 7}}\\m &= \frac{1}{2}\end{align}\]

(h)  \(\begin{align} 6z + 10 = - 2\end{align} \)

Transposing \(10\) to the R.H.S.

\[\begin{align}6z &= - 2 - 10\\z &= \frac{{ - 12}}{6}\\z& = - 2\end{align}\]

(i) \(\begin{align} \frac{{3l}}{2} = \frac{2}{3}\end{align} \)

\[\begin{align}l &= \frac{2}{3} \times \frac{2}{3}\\l &= \frac{4}{9}\end{align}\]

(j) \(\begin{align} \frac{{2b}}{3} - 5 = 3\end{align} \)

\[\begin{align}\frac{{2b}}{3} &= 3 + 5\\\frac{{2b}}{3} &= 8\\b &= 8 \times \frac{3}{2}\\b &= 12\end{align}\]

  
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