Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x+2)& = & -7 \color{red}{-} (14+x) \\\Leftrightarrow & -36x+12& = &-7-14-x \\\Leftrightarrow & -36x \color{red}{+12} & = &-21 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -36x+x& = &-21-12 \\\Leftrightarrow & -35x& = &-33 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-33}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{33}{35} & & \\ & V = \left\{ \frac{33}{35} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x-5)& = & 2 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x-30& = &2+11-x \\\Leftrightarrow & 30x \color{red}{-30} & = &13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &13+30 \\\Leftrightarrow & 31x& = &43 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{43}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{43}{31} & & \\ & V = \left\{ \frac{43}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-6)& = & -13 \color{red}{-} (-3+x) \\\Leftrightarrow & 36x-36& = &-13+3-x \\\Leftrightarrow & 36x \color{red}{-36} & = &-10 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 36x+x& = &-10+36 \\\Leftrightarrow & 37x& = &26 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{26}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{26}{37} & & \\ & V = \left\{ \frac{26}{37} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+2)& = & 9 \color{red}{+} (-1-5x) \\\Leftrightarrow & 36x+12& = &9-1-5x \\\Leftrightarrow & 36x \color{red}{+12} & = &8 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 36x+5x& = &8-12 \\\Leftrightarrow & 41x& = &-4 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-4}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-4}{41} & & \\ & V = \left\{ \frac{-4}{41} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-2)& = & -4 \color{red}{+} (-9+x) \\\Leftrightarrow & -30x-10& = &-4-9+x \\\Leftrightarrow & -30x \color{red}{-10} & = &-13 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -30x-x& = &-13+10 \\\Leftrightarrow & -31x& = &-3 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-3}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x-6)& = & -6 \color{red}{-} (-4+x) \\\Leftrightarrow & 20x-24& = &-6+4-x \\\Leftrightarrow & 20x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 20x+x& = &-2+24 \\\Leftrightarrow & 21x& = &22 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{22}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{22}{21} & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-2x-2)& = & -1 \color{red}{-} (-1-3x) \\\Leftrightarrow & -10x-10& = &-1+1+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &0 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &0+10 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+5)& = & -3 \color{red}{+} (9+x) \\\Leftrightarrow & 20x+20& = &-3+9+x \\\Leftrightarrow & 20x \color{red}{+20} & = &6 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &6-20 \\\Leftrightarrow & 19x& = &-14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-14}{19} & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-1)& = & -2 \color{red}{+} (-9+x) \\\Leftrightarrow & -2x-2& = &-2-9+x \\\Leftrightarrow & -2x \color{red}{-2} & = &-11 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -2x-x& = &-11+2 \\\Leftrightarrow & -3x& = &-9 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-9}{ \color{red}{-3} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x-2)& = & 8 \color{red}{-} (7-5x) \\\Leftrightarrow & 6x-6& = &8-7+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &1 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &1+6 \\\Leftrightarrow & x& = &7 \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x+2)& = & -7 \color{red}{+} (-7+2x) \\\Leftrightarrow & 15x+10& = &-7-7+2x \\\Leftrightarrow & 15x \color{red}{+10} & = &-14 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & 15x-2x& = &-14-10 \\\Leftrightarrow & 13x& = &-24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-5)& = & 11 \color{red}{+} (4+3x) \\\Leftrightarrow & -20x-25& = &11+4+3x \\\Leftrightarrow & -20x \color{red}{-25} & = &15 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -20x-3x& = &15+25 \\\Leftrightarrow & -23x& = &40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)