Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x+4)& = & 8 \color{red}{+} (6-5x) \\\Leftrightarrow & 6x+12& = &8+6-5x \\\Leftrightarrow & 6x \color{red}{+12} & = &14 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 6x+5x& = &14-12 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x-2)& = & -2 \color{red}{+} (9+x) \\\Leftrightarrow & -5x-10& = &-2+9+x \\\Leftrightarrow & -5x \color{red}{-10} & = &7 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -5x-x& = &7+10 \\\Leftrightarrow & -6x& = &17 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{17}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-17}{6} & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-5)& = & -4 \color{red}{-} (-8+x) \\\Leftrightarrow & 24x-30& = &-4+8-x \\\Leftrightarrow & 24x \color{red}{-30} & = &4 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &4+30 \\\Leftrightarrow & 25x& = &34 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{34}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{34}{25} & & \\ & V = \left\{ \frac{34}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+6)& = & 5 \color{red}{+} (2+4x) \\\Leftrightarrow & -15x+30& = &5+2+4x \\\Leftrightarrow & -15x \color{red}{+30} & = &7 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & -15x-4x& = &7-30 \\\Leftrightarrow & -19x& = &-23 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-23}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{23}{19} & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+3)& = & -5 \color{red}{-} (1-4x) \\\Leftrightarrow & -5x+15& = &-5-1+4x \\\Leftrightarrow & -5x \color{red}{+15} & = &-6 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &-6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -5x-4x& = &-6-15 \\\Leftrightarrow & -9x& = &-21 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-21}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x+2)& = & -10 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x+8& = &-10-9+x \\\Leftrightarrow & -12x \color{red}{+8} & = &-19 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &-19-8 \\\Leftrightarrow & -13x& = &-27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x-6)& = & 12 \color{red}{+} (1-5x) \\\Leftrightarrow & -6x-12& = &12+1-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &13 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &13+12 \\\Leftrightarrow & -x& = &25 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{25}{ \color{red}{-1} } \\\Leftrightarrow & x = -25 & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-6)& = & -15 \color{red}{-} (-4+x) \\\Leftrightarrow & -15x-18& = &-15+4-x \\\Leftrightarrow & -15x \color{red}{-18} & = &-11 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -15x+x& = &-11+18 \\\Leftrightarrow & -14x& = &7 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{7}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+4)& = & 9 \color{red}{+} (3-5x) \\\Leftrightarrow & 18x+24& = &9+3-5x \\\Leftrightarrow & 18x \color{red}{+24} & = &12 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 18x+5x& = &12-24 \\\Leftrightarrow & 23x& = &-12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x-3)& = & 10 \color{red}{+} (3+x) \\\Leftrightarrow & 24x-12& = &10+3+x \\\Leftrightarrow & 24x \color{red}{-12} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &13+12 \\\Leftrightarrow & 23x& = &25 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{25}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{25}{23} & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+7)& = & 7 \color{red}{-} (10+x) \\\Leftrightarrow & 36x+42& = &7-10-x \\\Leftrightarrow & 36x \color{red}{+42} & = &-3 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 36x+x& = &-3-42 \\\Leftrightarrow & 37x& = &-45 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-45}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-45}{37} & & \\ & V = \left\{ \frac{-45}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-5x+6)& = & -12 \color{red}{+} (-14+3x) \\\Leftrightarrow & -25x+30& = &-12-14+3x \\\Leftrightarrow & -25x \color{red}{+30} & = &-26 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &-26 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & -25x-3x& = &-26-30 \\\Leftrightarrow & -28x& = &-56 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-56}{ \color{red}{-28} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)