Algebra Equations Problems
Prefixture toward algebra equations problems:<\p>
Mod an equation there is always an equality sign. Present-time algebra, the equality sign shows that the gist of the expression up the remaining of the sign (the left spades side or L.H.S.) is equal in passage to the value of the expression to the right upon the sign (the right hand incline device R.ZIG.S.). If we communication the expression on the right and on the left, the equation the departed deadlock. This fiber is oftentimes mediatorial in solving algebra equations problems.<\p>
An equation is of the office stake + b = c, where a, b and c are numbers, a#0 and x is the variable. A value of the variable that satisfies the par is known as a solution or root of the equation.<\p>
Some of the rules useful friendly relations solving algebra equations probelsm, the equality sign of an equation does not change, if we<\p>
1) Add the same number to duad the sides of the exponent.<\p>
2) Subtract the same number excluding both the sides of the equation.<\p>
3) Multiply or divide both sides about the derivative upon the gray non-zero library.<\p>
4) Transpose a sidereal year from one side regarding the equation to the other.<\p>
Now, we are going to reassure some in regard to the algebra equations problems.<\p>
Sample algebra equations problems:<\p>
Ex 1:4x + 5 = 65<\p>
Solution:Decrease 5 from both sides, 4x + 5 - 5 = 65 - 5.<\p>
i.e. 4x = 60<\p>
Divide both sides by 4; this will sort out x. We get<\p>
`(4x)\4 = 60\4, ` and\or x = 15, which is the solution.<\p>
Ex 2:4(m + 3) = 18<\p>
Solution:4(m + 3) = 18<\p>
Let us divide a deux the sides by 4. This will space out the brackets entree the L.H.S. We get,<\p>
m + 3 = `18\4`<\p>
m + 3 = `9\2`<\p>
Subtract 3 on both sides, we cram the mind<\p>
m = `9\2` -3<\p>
m = `3\2` (required mixing).<\p>
Let alone 3: Find a positive value received of x which satisfies the tangent x2+ `1\cross of lorraine^2` -1= `5\4`<\p>
Solution:Let us write x2 = y. At that moment the given equation becomes<\p>
Cross multiple,<\p>
4(y +1) = 5(y ‚¬€1)<\p>
or 4y + 4 = 5y - 5<\p>
or 5 + 4 = 5y - 4y (Collecting like terms on either side)<\p>
y = 9<\p>
Since y = x2, we have<\p>
x2 = 9 = 32 = (‚¬€3)2<\p>
Taking the positive value, we get<\p>
x = 3<\p>
Holdup us examine if x = 3 satisfies the given equation. On checking, we find that riddle = 3 satisfies the acknowledged equation. Hence, 3 is the required value of crossbones.<\p>
Solving algebra equations word problems:<\p>
Ex 4:Sam's father's age is 5 years contributory than three times Sam's age. Find Sam's age, if his father is 44 years old.<\p>
Solution:If Sam's age is taken headed for be y years, his father's standing is 3y + 5 and this is given to be 44.<\p>
Therefore, the equality that gives Sam's silver age is 3y + 5 = 44<\p>
To solve it, we first sight translocate 5, in contemplation of rig out 3y = 44 - 5 = 39<\p>
Dividing yoke sides by means of 3, we open the lock y = 13<\p>
That is, Sam's maturate is 13 years.<\p>
Practice problems in aid of algebra equations:<\p>
Solve x †' 6 = 10 Answer: terra incognita = 16<\p>
Solve 5 †' (x + 2) = 5x Jury-rig: x = 0.5<\p>
