Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(4x-4)=4+(7+x)\)
2. \(2(5x-6)=-5-(13+x)\)
3. \(4(4x-3)=9+(4+x)\)
4. \(4(x-2)=9+(-14-3x)\)
5. \(6(4x-4)=13+(14+x)\)
6. \(2(-4x+2)=6+(14+x)\)
7. \(4(-x-6)=-10+(-11-3x)\)
8. \(2(x-7)=-6+(9+x)\)
9. \(5(x-3)=1+(3-4x)\)
10. \(3(-5x+4)=14+(-7+x)\)
11. \(4(-2x+4)=-3-(-3+x)\)
12. \(2(-x-3)=13-(-15+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x-4)& = & 4 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-12& = &4+7+x \\\Leftrightarrow & 12x \color{red}{-12} & = &11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &11+12 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-6)& = & -5 \color{red}{-} (13+x) \\\Leftrightarrow & 10x-12& = &-5-13-x \\\Leftrightarrow & 10x \color{red}{-12} & = &-18 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 10x+x& = &-18+12 \\\Leftrightarrow & 11x& = &-6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x-3)& = & 9 \color{red}{+} (4+x) \\\Leftrightarrow & 16x-12& = &9+4+x \\\Leftrightarrow & 16x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 16x-x& = &13+12 \\\Leftrightarrow & 15x& = &25 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{25}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-2)& = & 9 \color{red}{+} (-14-3x) \\\Leftrightarrow & 4x-8& = &9-14-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-5+8 \\\Leftrightarrow & 7x& = &3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x-4)& = & 13 \color{red}{+} (14+x) \\\Leftrightarrow & 24x-24& = &13+14+x \\\Leftrightarrow & 24x \color{red}{-24} & = &27 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &27+24 \\\Leftrightarrow & 23x& = &51 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{51}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{51}{23} & & \\ & V = \left\{ \frac{51}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-4x+2)& = & 6 \color{red}{+} (14+x) \\\Leftrightarrow & -8x+4& = &6+14+x \\\Leftrightarrow & -8x \color{red}{+4} & = &20 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -8x-x& = &20-4 \\\Leftrightarrow & -9x& = &16 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{16}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-6)& = & -10 \color{red}{+} (-11-3x) \\\Leftrightarrow & -4x-24& = &-10-11-3x \\\Leftrightarrow & -4x \color{red}{-24} & = &-21 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -4x+3x& = &-21+24 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-7)& = & -6 \color{red}{+} (9+x) \\\Leftrightarrow & 2x-14& = &-6+9+x \\\Leftrightarrow & 2x \color{red}{-14} & = &3 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 2x-x& = &3+14 \\\Leftrightarrow & x& = &17 \\ & V = \left\{ 17 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-3)& = & 1 \color{red}{+} (3-4x) \\\Leftrightarrow & 5x-15& = &1+3-4x \\\Leftrightarrow & 5x \color{red}{-15} & = &4 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 5x+4x& = &4+15 \\\Leftrightarrow & 9x& = &19 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{19}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{19}{9} & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+4)& = & 14 \color{red}{+} (-7+x) \\\Leftrightarrow & -15x+12& = &14-7+x \\\Leftrightarrow & -15x \color{red}{+12} & = &7 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -15x-x& = &7-12 \\\Leftrightarrow & -16x& = &-5 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-5}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{5}{16} & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x+4)& = & -3 \color{red}{-} (-3+x) \\\Leftrightarrow & -8x+16& = &-3+3-x \\\Leftrightarrow & -8x \color{red}{+16} & = &0 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -8x+x& = &0-16 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x-3)& = & 13 \color{red}{-} (-15+x) \\\Leftrightarrow & -2x-6& = &13+15-x \\\Leftrightarrow & -2x \color{red}{-6} & = &28 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -2x+x& = &28+6 \\\Leftrightarrow & -x& = &34 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{34}{ \color{red}{-1} } \\\Leftrightarrow & x = -34 & & \\ & V = \left\{ -34 \right\} & \\\end{align}\)