Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-3)& = & 6 \color{red}{-} (-4+x) \\\Leftrightarrow & 30x-18& = &6+4-x \\\Leftrightarrow & 30x \color{red}{-18} & = &10 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &10+18 \\\Leftrightarrow & 31x& = &28 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{28}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{28}{31} & & \\ & V = \left\{ \frac{28}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-2x-1)& = & 1 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x-6& = &1+7-x \\\Leftrightarrow & -12x \color{red}{-6} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &8+6 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x-2)& = & 3 \color{red}{+} (2+4x) \\\Leftrightarrow & -15x-6& = &3+2+4x \\\Leftrightarrow & -15x \color{red}{-6} & = &5 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & -15x-4x& = &5+6 \\\Leftrightarrow & -19x& = &11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-2x-2)& = & 2 \color{red}{+} (-11+3x) \\\Leftrightarrow & -4x-4& = &2-11+3x \\\Leftrightarrow & -4x \color{red}{-4} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -4x-3x& = &-9+4 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x+1)& = & 1 \color{red}{+} (-10+3x) \\\Leftrightarrow & 16x+4& = &1-10+3x \\\Leftrightarrow & 16x \color{red}{+4} & = &-9 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 16x-3x& = &-9-4 \\\Leftrightarrow & 13x& = &-13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-13}{ \color{red}{13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x+6)& = & 13 \color{red}{+} (-11+x) \\\Leftrightarrow & 24x+24& = &13-11+x \\\Leftrightarrow & 24x \color{red}{+24} & = &2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &2-24 \\\Leftrightarrow & 23x& = &-22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-5x-6)& = & -15 \color{red}{+} (-7-4x) \\\Leftrightarrow & -25x-30& = &-15-7-4x \\\Leftrightarrow & -25x \color{red}{-30} & = &-22 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{+4x} & = &-22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+30} \\\Leftrightarrow & -25x+4x& = &-22+30 \\\Leftrightarrow & -21x& = &8 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{8}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x+5)& = & -10 \color{red}{+} (-7-5x) \\\Leftrightarrow & -18x+30& = &-10-7-5x \\\Leftrightarrow & -18x \color{red}{+30} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & -18x+5x& = &-17-30 \\\Leftrightarrow & -13x& = &-47 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-47}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{47}{13} & & \\ & V = \left\{ \frac{47}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (x+7)& = & 6 \color{red}{-} (3+x) \\\Leftrightarrow & 2x+14& = &6-3-x \\\Leftrightarrow & 2x \color{red}{+14} & = &3 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 2x+x& = &3-14 \\\Leftrightarrow & 3x& = &-11 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-11}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+6)& = & -10 \color{red}{-} (2+x) \\\Leftrightarrow & 36x+36& = &-10-2-x \\\Leftrightarrow & 36x \color{red}{+36} & = &-12 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 36x+x& = &-12-36 \\\Leftrightarrow & 37x& = &-48 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-48}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-48}{37} & & \\ & V = \left\{ \frac{-48}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-2x+2)& = & 5 \color{red}{+} (4-5x) \\\Leftrightarrow & -6x+6& = &5+4-5x \\\Leftrightarrow & -6x \color{red}{+6} & = &9 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -6x+5x& = &9-6 \\\Leftrightarrow & -x& = &3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{3}{ \color{red}{-1} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x-7)& = & -5 \color{red}{+} (8+x) \\\Leftrightarrow & -12x-42& = &-5+8+x \\\Leftrightarrow & -12x \color{red}{-42} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -12x-x& = &3+42 \\\Leftrightarrow & -13x& = &45 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{45}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-45}{13} & & \\ & V = \left\{ \frac{-45}{13} \right\} & \\\end{align}\)