How To Learn Algebra With Pictures

You don’t necessarily need to be great at doing these basic operations in your head to do algebra problems. Many algebra classes will allow you to use a calculator to save time when doing these simple operations. You should, however, at least know how to do these operations without a calculator for when you aren’t allowed to use one.

Parentheses Exponents Multiplication Division Addition Subtraction The order of operations is important in algebra because doing the operations in an algebra problem in the wrong order can sometimes affect the answer. For instance, if we’re dealing with the math problem 8 + 2 × 5, if we add 2 to 8 first, we get 10 × 5 = 50, but if we multiply 2 and 5 first, we get 8 + 10 = 18. Only the second answer is correct.

On a number line, a negative version of a number is the same distance from zero as the positive, but in the opposite direction. Adding two negative numbers together makes the number more negative (in other words, the digits will be higher, but since the number is negative, it counts as being lower) Two negative signs cancel out — subtracting a negative number is the same as adding a positive number Multiplying or dividing two negative numbers gives a positive answer. Multiplying or dividing a positive number and a negative number gives a negative answer.

For example, to solve the equation 9/3 - 5 + 3 × 4, we might keep our problem organized like this: 9/3 - 5 + 3 × 4 9/3 - 5 + 12 3 - 5 + 12 3 + 7 10

Letters like x, y, z, a, b, and c Greek letters like theta, or θ Note that not all symbols are unknown variables. For instance, pi, or π, is always equal to about 3. 14159.

For example, in the equation 2x + 3 = 11, x is our variable. This means that there’s some value that goes in the place of x to make the left side of the equation equal 11. Since 2 × 4 + 3 = 11, in this case, x = 4. An easy way to start understanding variables is to replace them with question marks in algebra problems. For example, we might re-write the equation 2 + 3 + x = 9 as 2 + 3 + ? = 9. This makes it easier to understand what we’re trying to do — we just need to find out what number to add to 2 + 3 = 5 to get 9. The answer is again 4, of course.

For example, let’s look at the equation 2x + 1x = 9. In this case, we can add 2x and 1x together to get 3x = 9. Since 3 x 3 = 9, we know that x = 3. Note again that you can only add the same variables together. In the equation 2x + 1y = 9, we can’t combine 2x and 1y because they are two different variables. This is also true for when one variable has a different exponent than another. For instance, in the equation 2x + 3x2 = 10, we can’t combine 2x and 3x2 because the x variables have different exponents. See How to Add Exponents for more information.

In the example (x + 2 = 9 × 4), to get x by itself on the left side of the equation, we need to get rid of the “+ 2”. To do this, we’ll simply subtract 2 from that side, leaving us with x = 9 × 4. However, to keep both sides of the equation equal, we also need to subtract 2 from the other side. This leaves us with x = 9 × 4 - 2. Following the order of operations, we multiply first, then subtract, giving us an answer of x = 36 - 2 = 34.

In general, addition and subtraction are like “opposites” — do one to get rid of the other. See below: For addition, subtract. Example: x + 9 = 3 → x = 3 - 9 For subtraction, add. Example: x - 4 = 20 → x = 20 + 4

With multiplication and division, you must perform the opposite operation on everything on the other side of the equals sign, even if it’s more than one number. See below: For multiplication, divide. Example: 6x = 14 + 2→ x = (14 + 2)/6 For division, multiply. Example: x/5 = 25 → x = 25 × 5

It may be a little confusing, but, in these cases, you take the root of both sides when dealing with an exponent. On the other hand, you take the exponent of both sides when you’re dealing with a root. See below: For exponents, take the root. Example: x2 = 49 → x = √49 For roots, take the exponent. Example: √x = 12 → x = 122

For example, let’s solve the equation x + 2 = 3 by using boxes (☐) x +2 = 3 ☒+☐☐ =☐☐☐ At this point, we’ll subtract 2 from both sides by simply removing 2 boxes (☐☐) from both sides: ☒+☐☐-☐☐ =☐☐☐-☐☐ ☒=☐, or x = 1 As another example, let’s try 2x = 4 ☒☒ =☐☐☐☐ At this point, we’ll divide both sides by two by separate the boxes on each side into two groups: ☒|☒ =☐☐|☐☐ ☒ = ☐☐, or x = 2

For example, let’s say we’re told that a football field is 30 yards (27. 4 m) longer than it is wide. We use the equation l = w + 30 to represent this. We can test whether this equation makes sense by plugging in simple values for w. For instance, if the field is w = 10 yards (9. 1 m) wide, it will be 10 + 30 = 40 yards (36. 6 m) long. If it’s 30 yards (27. 4 m) wide, it will be 30 + 30 = 60 yards (54. 9 m) long, and so on. This makes sense — we’d expect the field to get longer as it gets wider, so this equation is reasonable.

For instance, let’s say that we narrow down an algebra equation to x = 12507. If we type 12507 into a calculator, we’ll get a huge string of decimals (plus, since the calculator’s screen is only so large, it can’t display the entire answer. ) In this case, we may want to represent our answer as simply 12507 or else simplify the answer by writing it in scientific notation.

Equations with the form ax + ba factor to a(x + b). Example: 2x + 4 = 2(x + 2) Equations with the form ax2 + bx factor to cx((a/c)x + (b/c)) where c is the biggest number that divides into a and b evenly. Example: 3y2 + 12y = 3y(y + 4) Equations with the form x2 + bx + c factor to (x + y)(x + z) where y × z = c and yx + zx = bx. Example: x2 + 4x + 3 = (x + 3)(x + 1).

If, for some reason, your teacher can’t help you, try asking them about tutoring options at your school. [11] X Expert Source Daron CamAcademic Tutor Expert Interview. 29 May 2020. Many schools will have some sort of after-school program that can help you get the extra time and attention you need to start excelling at your algebra. Remember, using free help that’s available to you isn’t something to be embarrassed about — it’s a sign that you’re smart enough to solve your problem!

For example, in the equation y = 3x, if we plug in 2 for x, we get y = 6. This means that the point (2,6) (two spaces to the right of center and six spaces above center) is part of this equation’s graph. Equations with the form y = mx + b (where m and b are numbers) are especially common in basic algebra. These equations always have a slope of m and cross the y axis at y = b.

For instance, with the equation 3 > 5x - 2, we would solve just like we would for a normal equation: 3 > 5x - 2 5 > 5x 1 > x, or x < 1. This means that every number less than one works for x. In other words, x can be 0, -1, -2, and so on. If we plug these numbers into the equation for x, we’ll always get an answer less than 3.

As an example, let’s solve the quadratic formula 3x2 + 2x -1 = 0. x = [-b +/- √(b2 - 4ac)]/2a x = [-2 +/- √(22 - 4(3)(-1))]/2(3) x = [-2 +/- √(4 - (-12))]/6 x = [-2 +/- √(16)]/6 x = [-2 +/- 4]/6 x = -1 and 1/3

For example, let’s say we’re working with a system that contains the equations y = 3x - 2 and y = -x - 6. If we draw these two lines on a graph, we get one line that goes up at a steep angle, and one that goes down at a mild angle. Since these lines cross at the point (-1,-5), this is a solution to the system. [13] X Research source If we want to check our problem, we can do this by plugging our answer into the equations in the system — a right answer should “work” for both. y = 3x - 2 -5 = 3(-1) - 2 -5 = -3 - 2 -5 = -5 y = -x - 6 -5 = -(-1) - 6 -5 = 1 - 6 -5 = -5 Both equations “check out,” so our answer is right!