Algebra Class - Expression Calculations

To solve this problem, we must follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

This problem involves subtracting a negative number, which is the same as adding the positive version of that number. So, (-2) - (-2) becomes (-2) + 2.

The equation involves multiplying a negative number by a positive number. The result is always negative.

The problem involves dividing a positive number by a negative number. The result is always negative.

The absolute value of a number is its distance from zero, regardless of whether it's positive or negative. Therefore, the absolute value of -4 is 4.

Adding fractions with different denominators involves finding a common denominator, then adding the numerators.

Subtracting fractions with different denominators requires finding a common denominator, then subtracting the numerators.

A fraction with a negative sign in the numerator can be rewritten with the negative sign in the denominator.

When dividing fractions, flip the second fraction and multiply.

Simplify fractions by finding the greatest common factor (GCF) and dividing both the numerator and denominator by it.

The Least Common Multiple (LCM) is the smallest positive integer that is a multiple of two or more given integers.

To compare fractions, we need to ensure they have the same denominator. We can express both fractions with a common denominator, and then compare their numerators.

Adding fractions with different denominators requires making them equivalent with a common denominator. Find the common denominator and then add the numerators.

Multiplying mixed numbers involves converting the mixed number to an improper fraction and then multiplying.

To find the Least Common Multiple (LCM) of algebraic expressions, we identify the highest powers present for each variable in the given expressions and multiply them together.

Changing the order of addends (numbers being added) doesn't change the sum.

Changing the order of factors (numbers being multiplied) doesn't change the product.

Multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products.

Grouping the addends differently does not affect the sum.

Multiplying any number by 1 results in the same number.

The process of combining like terms and simplifying the expression by following order of operations.

A numerical or variable quantity placed before and multiplying another quantity, as in 3x, where 3 is the coefficient of x.

Terms that have the same variable raised to the same power, allowing them to be added or subtracted.

Involves adding or subtracting expressions by combining like terms, following the order of operations.

Combining like terms involves adding or subtracting terms that have the same variable and exponent. For example, 2x + 3x simplifies to 5x.

To solve an equation, you need to isolate the variable on one side of the equation. This is done by performing the same operation on both sides of the equation to maintain equality. For example, to solve x + 2 = 5, subtract 2 from both sides.

To simplify an expression, you need to combine like terms, distribute, and follow the order of operations (PEMDAS/BODMAS). For example, 2x + 3 - 4x + 5 simplifies to -2x + 8.

A proportion is an equation stating that two ratios are equal. To solve a proportion, you can use cross-multiplication.

A unit rate is a rate in which the second quantity is one unit. To find a unit rate, divide the first quantity by the second quantity.

To solve a proportion problem, you need to identify the unknown value and set up the proportion. Cross-multiply to solve for the unknown.

Similar figures have the same shape but different sizes. The corresponding sides of similar figures are proportional.

A map scale is a ratio that compares the distance on a map to the actual distance on the ground.

Equations where variables appear in the denominator. They often require specific steps for solving, such as cross-multiplication or finding a common denominator.

A method to solve rational equations by multiplying both sides of the equation by the least common multiple of the denominators.

A technique for simplifying expressions by finding the greatest common factor (GCF) of the numerator and denominator, then dividing both by the GCF.

Special cases of rational equations that can be solved by factoring and then canceling out common factors.

A negative sign in front of parentheses means we multiply the inside values by -1. To solve -(-12/4), we multiply (-1) by (-12/4) resulting in 3. Then we subtract 50 from 3, which equals -47. Finally, we add -25 to -47, resulting in -72. Therefore, the final answer is -72.

The absolute value of a number is its distance from zero, always a positive value. Therefore, |-5| = 5. Then we multiply (-3 ) by 5, resulting in -15. To solve -(-3 x 5), we multiply -1 by (-15), resulting in 15. Hence, the box represents the inequality sign >.

Remember, parenthesis are solved first. To solve -3 -2 + (-6), we combine them as -3 -2 + (-6) = -11. Next, we simplify (4 x -10)/(2 x -1) which equals -40/-2, and then simplifies to 20. Finally, we solve: -11 + 20 - (3 x -4), which equals -11 + 20 + 12 = 21. Therefore, the final answer is 21.

Substitute a = -2 and b = 3 in the expression: 4[3(a-2)] - b. First, substitute a = -2 in the expression 4[3(a - 2)] to get 4[3(-2 - 2)]. Simplify inside the parentheses to get 4[3(-4)], and then 4[-12]. Finally, we get -48 - 3 = -51. So the expression evaluates to -51.

Order of operations tells us to simplify expressions within parentheses first. To solve 3(a-2) with a=-2, we get 3 * (-2 - 2), or 3 * (-4), which equals -12. Then multiply -12 by 4, resulting in -48.
Finally, subtract 3 to get -51. Therefore, the expression evaluates to -51.

To get x by itself, we need to isolate it on one side of the equation. In this case, we subtract 9 from both sides and simplify: -x = -21. Then we solve for x by multiplying both sides by -1: x = 21.

To isolate x, we need to eliminate the constant term (-15) and the coefficient of x (1/7). We add 15 to both sides and then multiply both sides by 7. The equation becomes x = 28.

To isolate x, we first distribute 1/5 on the left and -1/2 on the right side. This gives us -2x - 3 = 4x - 2. Next, we combine like terms by adding 2x to both sides and adding 2 to both sides, getting -1 = 6x. Finally, we divide both sides by 6 and simplify: x = -1/6.

To isolate x, we need to eliminate the fraction by multiplying both sides by 5 and 2. This results in -2(-10x-15) = -1(-8x+4). Next, distribute -2 on the left and -1 on the right, giving us 20x + 30 = 8x - 4. Combining like terms by subtracting 8x from both sides and subtracting 30 from both sides gives us 12x = -34. Finally, we divide both sides by 12 and simplify: x = -17/6.