Question

Please help, I and I also need a thorough explanation, I don't understand this

Answer 1

Answer:

See below ↓

Step-by-step explanation:

Solve for x.

2.1.1

• px + qx = a
• x (p + q) = a
• x = a / (p + q)

2.1.2

• 2x² - 5x + 2 = 0
• 2x² - 4x - x + 2 = 0
• 2x(x - 2) - 1(x - 2) = 0
• (2x - 1)(x - 2) = 0
• x = 1/2, 2

2.1.3

• $(\frac{1}{2} )^{3x+1}$ = 32
• $2x^{-3x-1} = 2^{5}$
• -3x - 1 = 5
• -3x = 6
• x = -2

I can only answer 3 questions together at maximum so kindly post the rest of your questions 3 at a time separately.

Hope this helped~

Answer 2

Answer:

x = a/(p+q)

x = 2 or x = 1/2

x = -2

m≤ -1 or m<4

-1 , 0 , 1 , 2 and 3.....................since : -1 ≥ m < 4.

x = -3 and y = 9.

Step-by-step explanation:

The first one is just making x to be the subject of the formula by factorising p and q. Then dividing both sides by (p + q).

px + qx = a........................... x (p + q) = a............divide sides by ( p+q) to get the expression.

Solve quadratically for the second one.

For the third one, apply the laws of indices to work out.

32 = ( 1/2)^-5..............so, ( 1/2)^3x + 1   = ( 1/2)^-5.......Drop the base numbers since they are common.

3x + 1 = -5.........then solve to get x as -2.

For the fourth one, we solve for m by separating it into 2.

the first one is: -11 ≤ 3m - 8.

the second one: 3m - 8 < 4

then solve like a normal equation but maintain the inequality signs.

For the integral values, you'll get them from the answers because the answers are a range

The last one you solve simultaneously either by substitution or elimination method.

HOPE THIS HELPS