how to solving equations and inequalities?
606768
['Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.', 'But these things will change direction of the inequality: ... ', "Don't multiply or divide by a variable (unless you know it is always positive or always negative)"]
671516
When graphing a linear inequality on a number line, use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to". The solution set for this problem will be all values that satisfy both -3 < x and x < 4.
1420207
['Example 1 – Solve: x2 + 16 = 10x.', 'Example 2 – Solve: 18x2 – 3x = 6.', 'Example 3 – Solve: 50x2 = 72.', 'Example 4 – Solve: x(2x – 1) = 3.', 'Example 5 – Solve: (x + 3)(x – 5) = –7.', 'Example 6 – Solve: 3x(x + 1) = (2x + 3)(x + 1)']
1441672
Now we can solve a Quadratic Equation in 5 steps: Step 1 Divide all terms by a (the coefficient of x2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
1352154
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound inequality. This holds true for all absolute value inequalities. You can replace > above with ≥ and < with ≤.
303687
To graph a quadratic inequality, start by graphing the parabola. Then fill in the region either above or below it, depending on the inequality. If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.
1037224
Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number. Swapping left and right hand sides.
32727
['Step 1 Divide all terms by a (the coefficient of x2).', 'Step 2 Move the number term (c/a) to the right side of the equation.', 'Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.']
439015
['First, replace f(x) with y . ... ', 'Replace every x with a y and replace every y with an x .', 'Solve the equation from Step 2 for y . ... ', 'Replace y with f−1(x) f − 1 ( x ) .']
1034941
A quadratic equation contains terms up to . There are many ways to solve quadratics. All quadratic equations can be written in the form a x 2 + b x + c = 0 where , and are numbers ( cannot be equal to 0, but and can be).
1286082
There is another method, called the test point method, that can be used instead of the sign graph to solve inequalities. The following example shows how to solve a quadratic inequality that involves a prime polynomial. Solve x2 - 4x - 6 > 0 and graph the solution set.
407184
To solve for x when the equation includes an exponent, start by isolating the term with the exponent. Then, isolate the variable with the exponent by dividing both sides by the coefficient of the x term to get your answer. If the equation has fractions, start by cross-multiplying the fractions.
53510
In algebra, an equation is a mathematical expression that contains an equals sign. It tells us that two expressions represent the same number. For example, y = 12x is an equation. An inequality is a mathematical expression that contains inequality signs.
870082
['What we need to do is simply set each factor equal to zero, and solve each equation for x.', 'The answers are x = − 7 x = - \\,7 x=−7 and x = 2 x = 2 x=2. ... ', 'The left side of the equation is a binomial. ... ', 'Note, I can also factor out 2 x 2x 2x instead of −2x.']
908556
["x(13âˆ'4x)=0,", '7(y+12)=0,', "(xâˆ'19)(x+3)=0,", "(yâˆ'6)(3zâˆ'4)=0."]
893523
['Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient. ... ', 'Step 2: Subtract the second equation from the first.', 'Step 3: Solve this new equation for y.', 'Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.']
199103
['Step 1: Getting Started. You should know that a quadratic equation looks something like this: x^2-3x+2=0 or ax^2+bx+c=0. ... ', 'Step 2: The Equation. Look at the first picture and put that on your calculator. ... ', 'Step 3: Displaying Results. Press program, then the right arrow, then 3. ... ', 'Step 4: Using the Program.']