''What is an equation?''
For example:
\(x+3=12\)
Consider an example:
(i) The product of five and a number is \(15\).
Now go step by step, multiply \(5\) and \(x.\)
That means \(5x\)
The result is \(15\).
So, we can write
\(5x=15\)
This is the required equation.
A \(5+x=20\)
B \(4x=20\)
C \(4-x=20\)
D \(\dfrac{x}{4}=20\)
For example: Solve for \(x\);
\(x+8 = 12\)
We know that the inverse operation of addition is subtraction.
Thus, we will subtract \(8\) from both sides of the equation to get only the variable on one side.
\(x+ \not{8}- \not{8} = 12-8\)
\(\Rightarrow x=4\)
Inverse operation: An inverse operation is the opposite of the given operation.
For example: Solve for \(z; \)
\(z-9=25\)
We know that the inverse operation of subtraction is addition.
Thus, we will add \(9\)to both sides of the equation to get only the variable on one side.
\(z- \not{9}+ \not{9} = 25+9\)
\(\Rightarrow z=34\)
Look at an example:
Olive has some pencils and some pens, altogether \(20.\) To write it in equation form, identify the important elements:
(i) Here, the number of pens and pencils are two unknown quantities, so we use two variables, \(x\) and \(y.\)
(ii) Altogether means addition.
(iii) "Is" means equals.
Now go step by step, add \(x\) and \(y.\)
That means \(x+y\)
The result is \(20\).
\(\therefore\) We can write,
\(x+y=20\)
This is the required equation.
A \(x-y=20\)
B \(x+y=10\)
C \(\dfrac{x}{y}=10\)
D \(xy=10\)
For example: Solve for \(b;\;2b=4\)
We know that the inverse operation of multiplication is division.
Thus, we will divide by \(2\) on both sides of the equation to get only the variable on one side.
\(\dfrac{ \not{2}b}{ \not{2}} = \dfrac{ \not{4}^2}{ \not{2}}\)
\(\Rightarrow b=2\)
For example: Solve for \(y:\; \dfrac{2}{y}=1\)
We know that the inverse operation of division is multiplication.
Thus, we will multiply the denominator \((y)\) with the value \((1)\) on the right side of the equation to get only the variable on one side.
\(\dfrac{2}{y}=\nearrow1\)
\(\Rightarrow\; 2= 1 ×y \)
\(\Rightarrow\; 2 =y\)
A \(2x=32\)
B \(3x+5 = 32\)
C \(2x+5=32\)
D \(5x+2 = 32\)