Q&A for How to Solve for X

Start on the side of the equation with X and do the inverse operations to isolate X. For example, if the equation was X + 5 = 10, you would subtract 5 from each side.

If the problem is 15:1,000 = x:100, re-write it as one fraction equal to another: 15 / 1,000 = x / 100. Solve for x either by inspection or by cross-multiplication.

Let x be the son's current age. Then 2x is Peter's current age. Twelve years ago the son's age was (x-12), and Peter's age was (2x-12). Set up an equation stating that Peter's age 12 years ago was four times the son's age then. Solve for x and 2x.

If you are told to find the value of something, let that "something" be x. For example, suppose there are two trees next to the beach. George planted a number of trees there. Now the total number of trees is 4. How many trees did George plant? Since you do not know the number of trees George planted, that number is x in your equation. Now you have x + 2 = 4. Solve for x, and you get x = 2. Thus the answer is George planted two trees. Use the same approach for other word problems.

Re-write slightly: (0.75x - 0.025314) / 0.0908 = 0.12. First multiply both sides of the equation by 0.0908 to get rid of the fraction: 0.75x - 0.025314 = (0.12)(0.0908) = 0.010896. Now add 0.025314 to both sides: 0.75x = 0.03621. Divide both sides by 0.75: x = 0.04828.

Add 16 to both sides of the equation, and you get X = 39.

There is no integer that could serve as an exponent to raise 4 to 8. Therefore, the exponent (x) has to be a fraction. In this case, you would solve by inspection: if you raise 4 to the third power, you get 64. The square root of 64 is 8. So if you raise 4 to the power of 3/2 (which means cubing 4 and then taking the square root of the result), you get 8. x = 3/2.

The equation is stated a bit awkwardly. If we assume the equation is 2 + 2 - 4x = 12, it becomes 4 -4x = 12. Subtract 4 from both sides: -4x = 8. Divide both sides by (-4), leaving x = -2. (If we assume the original equation is (2)(2) - 4x = 12, it becomes 4 - 4x = 12 and the solution is the same.)

Multiply the numerator by the whole number, and then divide by the denominator. Thus, 4 x 8 = 32, divided by 5 = 6.4.

Subtract 12g from both sides of the equation: -6 = g.

Choose some small values for x, calculate the corresponding values for y, and plot the x-y pairs on a graph. It will be a straight line at a 45° angle (lower left to upper right), elevated three units vertically above the origin of the coordinate plane.

Multiply them together to get x^2 +2x-15=9, then subtract 9 to get x^2+2x-24=0. The only numbers that add up to 2 and equal 24 when multiplied are -4 and 6. Write it as (x-4)(x+6) = 0. So, x must be 4 or -6.

Solve this by dividing 5/6 by 9/10. 5/6 ÷ 9/10 = (5/6)(10/9) = 50/54 = 25/27. So 5/6 divided by 25/27 equals 9/10.

You can't solve this, because it's not an equation. You can, however, evaluate the expression to some extent: x(x + 11) + 14 = x² + 11x + 14. That trinomial won't factor, so you're done.

4 = 2². Therefore, 4^(x-1) = 2^2(x-1). We're given that 2^(x+3) = 2^2(x-1). If 2^a = 2^b, a and b are equal. Therefore, x+3 = 2(x-1). So x+3 = 2x-2. Subtract x from both sides of that equation, and add 2 to both sides, so that x = 5. Verify by plugging 5 into the original equation: does 2^(5+3) equal 4^(5-1)? Yes. 2^8 = 256, and 4^4 = 256. So x does equal 5.

Combine like terms, so that -12x + 16 = 0. Add 12x to both sides: 16 = 12x. Divide both sides by 12: 16/12 = x. Reduce: x = 4/3. Verify by plugging that value of x back into the original equation. (Use the first simplified equation where like terms were combined.)

The difference between the first two terms is +8. The difference between the second and third terms is (8k -8). If this is an arithmetic sequence, +8 must equal (8k - 8). That means k = 2. That makes the sequence -2, 6, 14 (which is an arithmetic sequence).

Add 12 to each side, leaving 5x = 25. Divide each side by 5, and x = 5.

16 = 2^4. Therefore, 16³ = (2^4)³ = 2^12. So if 16³ = 2^12 = 2^3x, then 3x = 12, and x=4.

One practical way of solving this is trial and error: just try various convenient numbers for x until you solve the equation. As it happens, the square root of 81 is 9, and the square root of 9 is 3. Therefore, 3 raised to the fourth power is 81. Another way of solving exponential equations like this is using logarithms and with a calculator; take the 3-log of both sides to get x= 3-log(81). Plugging this into a calculator gives x=4. But solving via inspection as first mentioned is a valid approach as well, and one that doesn't require a calculator at that.

Substitute y/2 for x in the equation: 44 + y/2 = y. Subtract y/2 from both sides: 44 = y - (y/2) = y/2 = 44. Then y = 88.

The equation as you've written it does not work. Perhaps you meant 3x² - 5x - 2 = 0. In that case, (3x + 1)(x - 2) = 0. Then x = 2, and x = - 1/3.

7x - (x - 5) = 7x - x + 5 = 6x + 5 ≥ 14. 6x ≥ 9. x ≥ 1½. (Work with the ≥ sign the same way you work with the = sign.)

Let's assume the equation can be written 102 - (20x)/2 = 62. Then 40 - 10x = 0, and 40 = 10x. So x = 4.

1 / 4 = x / 6. Cross-multiply: (1)(6) = (4)(x) or 6 = 4x. Divide both sides by 4: 6/4 = x = 3/2.

See Solve Two Step Algebraic Equations and related articles.

The square root of 25 is equal to 5, because 5 times 5 = 25.

Let's assume the equation is 2x - 1/6 = x + (1/3)x. Then 2x - 1/6 = (4/3)x. Subtract (4/3)x from both sides: (2/3)x - 1/6 = 0. Add (1/6) to both sides: (2/3)x = 1/6. Multiply both sides by (3/2): x = 3/12 = 1/4.

Subtract 0.5x from both sides of the equation, and you get 0.5x = 20. Multiply both sides by 2: x = 40.

Multiply both sides by x. 686 = 7x. Divide both sides by 7. 98 = x.