Download Equations - bilingual project albujaira school

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EQUATION
ECUACIÓN
VARIABLE
INCÓGNITA
TERMS
TÉRMINOS
COEFFICIENTS
COEFICIENTES
CONSTANTS
CONSTANTES
DEGREE
GRADO
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3X – 7 = X + 5
LEFT SIDE
RIGHT SIDE
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3X – 7 = X + 5
TERMS: 3X; 7; X; 5
VARIABLE : X
COEFFICIENTS: 3 AND 1
CONSTANTS: 7 AND 5
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
The degree of an equation that has not
more than one variable in each term is
the exponent of the highest power to
which that variable is raised in the
equation.

The equation
3x - 17=0
is a FIRSTDEGREE equation, since x is raised only to
the first power.
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
Solving an equation for one variable
means finding the value of the variable
that makes the equation true.

For example, 11 is the SOLUTION of
x-7=4
since 11 - 7 = 4.
The number 11 is said to SATISFY the
equation
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Two equations are equivalent if they have the same
solution


We can create equivalent equations using the
following methods:
 Add or subtract the same quantity on either side of an
equation
 Multiply or divide both sides of an equation by the same
quantity.
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Let’s create equations equivalent to 5x = 20 using the methods
mentioned above

· Add 3 to each side
5x + 3 = 20 + 3 gives rise to 5x + 3 = 23
· Subtract 2 from each side
5x – 2 = 20 – 2 produces an equivalent equation 5x – 2 = 18
· Multiply each side by 4.
5x · 4 = 20 · 4 gives rise to 20x = 80
· Divide each side by 5.
5x ÷ 5 = 20 ÷ 5 gives rise to an equivalent equation
x=4
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
In general, to solve an equation the
following steps must be followed:
1. Remove parentheses.
2. Remove denominators.
3. Group the terms of x in one side and
the independent terms in the other.
4. Reduce similar terms.
5. Solve for the unknown.
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2X – 3 = 6 + X
 Group
the similar terms, and then add:
2X – X = 6 + 3
x=9
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2(2X – 3) = 6+ X
 Remove parentheses:
4X – 6 = 6 + X
 Group the terms and add:
4X – X = 6 + 6
3X = 12
 If both sides of the equation are divided
by 3, the solution is obtained:
X=4
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Jeanne has $17 in her piggy bank. How much money
does she need to buy a game that costs $68?
Solution:
Let x represent the amount of money Jeanne needs.
The following equation can represent this problem:

17 + x = 68
We can subtract 17 from both sides of the equation to
find the value of x.
68 - 17 = x
Answer:
x = 51, so Jeanne needs $51 to buy the game.
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