## Linear equations with one unknown

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

5-(7*x-4)=0

### Step by step solution :

### Step 1 :

#### Solving a Single Variable Equation :

1.1 Solve : -7x+9 = 0

Subtract 9 from both sides of the equation :

-7x = -9

Multiply both sides of the equation by (-1) : 7x = 9

Divide both sides of the equation by 7:

x = 9/7 = 1.286

### One solution was found :

x = 9/7 = 1.286## If for the functi

We have to find the value of λ given in the real function and we are given with the differentiability of the function f(x) = λx^{2} + 7x - 4 at x = 5 which is f ‘(5) = 97, so we will adopt the same process but with a little variation.

So by using the formula, f ‘(c) =, we get,

f ‘(5) =

f ‘(5) =

f ‘(5) =

f ‘(5) =

as the limit has some finite value, then there must be the formation of some indeterminate form like, so if we put the limit value, then the numerator will also be zero as the denominator, but there must be a factor (x - 5) in the numerator, so that this form disappears.

f ‘(5) =

f ‘(5) = lim_{x}_{→}_{5}λx + 5λ + 7 = 97

f ‘(5) = 10λ + 7 = 97

10λ = 90

λ = 9

## Linear equations with one unknown

### Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2/7*x-4-(5)=0

### Step by step solution :

### Step 1 :

2 Simplify — 7#### Equation at the end of step 1 :

2 ((— • x) - 4) - 5 = 0 7### Step 2 :

#### Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 7 as the denominator :

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

#### Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

#### Equation at the end of step 2 :

(2x - 28) ————————— - 5 = 0 7### Step 3 :

#### Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 7 as the denominator :

### Step 4 :

#### Pulling out like terms :

4.1 Pull out like factors :

2x - 28 = 2 • (x - 14)

#### Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

#### Equation at the end of step 4 :

2x - 63 ——————— = 0 7### Step 5 :

#### When a fraction equals zero :

5.1 When a fraction equals zero ...Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

Now, on the left hand side, the 7 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2x-63 = 0

#### Solving a Single Variable Equation :

5.2 Solve : 2x-63 = 0

Add 63 to both sides of the equation :

2x = 63

Divide both sides of the equation by 2:

x = 63/2 = 31.500

### One solution was found :

x = 63/2 = 31.500Pain. My legions are marching no easier to stop than Breakthrough from the lowest limits. Pain. The old generation is afraid of me.

## 4/5 7x

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