Page 123 - Start Up Mathematics_7
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At a Glance
1. An equation is a condition on a variable. It is a statement of equality having one or more
variables.
2. A linear equation is one in which the highest power of the variable(s) is one. It involves
only linear polynomials.
3. The value of the variable which satisfies the equation is called the solution or root of the
equation.
4. To maintain balance or equality in an equation, we can
(a) add same number on both sides. (b) subtract same number on both sides.
(c) multiply both sides by the same number. (d) divide both sides by same non-zero number.
5. Transposing means moving a term from one side to the other. Whenever a constant or variable
term is moved from one side to the other, its sign changes. Transposing a number has the
same effect as adding or subtracting a constant on both sides.
6. In systematic method of solving an equation, we perform identical mathematical operations
on both sides of the equation to obtain the solution of the variable.
7. An equation remains same if its LHS and RHS are interchanged.
Review Exercises
Multiple ChoiCe Questions
1. The solution of the equation 3x + 7 = 13 is:
(a) 1 (b) –1 (c) 2 (d) 3
2. Two supplementary angles are such that one is 60 less than the other. The greater of the two
angles is:
(a) 60° (b) 80° (c) 100° (d) 120°
3. The length and breadth of a rectangle are in the ratio 3 : 1. If the perimeter of the rectangle is
72 m, then the length of the rectangle is:
(a) 9 m (b) 18 m (c) 27 m (d) 36 m
4. An equation having x = –3 as its solution is:
(a) 2x + 8 = 2 (b) 2x + 8 = 3 (c) 2x + 7 = 2 (d) 5x = 14
solve Mentally
True or False
1. In a linear equation, the maximum power of a variable is one.
2. A linear equation in one variable can have many solutions.
3. While solving an equation, we can multiply one side and divide the other by the same constant.
4. From a given solution, infinite number of equations can be constructed.
5. 4x + 1 > 3x – 2 is a linear equation in one variable.
6. To balance an equation, we have to perform the same operation on both sides.
7. An equation changes if its LHS and RHS are interchanged.
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