Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (6x+7)& = & -8 \color{red}{-} (-9+x) \\\Leftrightarrow & 30x+35& = &-8+9-x \\\Leftrightarrow & 30x \color{red}{+35} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 30x+x& = &1-35 \\\Leftrightarrow & 31x& = &-34 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-34}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-34}{31} & & \\ & V = \left\{ \frac{-34}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-3)& = & 10 \color{red}{-} (-5+x) \\\Leftrightarrow & 10x-6& = &10+5-x \\\Leftrightarrow & 10x \color{red}{-6} & = &15 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 10x+x& = &15+6 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+5)& = & -6 \color{red}{+} (-7-5x) \\\Leftrightarrow & 18x+15& = &-6-7-5x \\\Leftrightarrow & 18x \color{red}{+15} & = &-13 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 18x+5x& = &-13-15 \\\Leftrightarrow & 23x& = &-28 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-28}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-28}{23} & & \\ & V = \left\{ \frac{-28}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-5)& = & -15 \color{red}{-} (8+x) \\\Leftrightarrow & 30x-25& = &-15-8-x \\\Leftrightarrow & 30x \color{red}{-25} & = &-23 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 30x+x& = &-23+25 \\\Leftrightarrow & 31x& = &2 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{2}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{2}{31} & & \\ & V = \left\{ \frac{2}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-1)& = & 8 \color{red}{+} (3+x) \\\Leftrightarrow & 12x-2& = &8+3+x \\\Leftrightarrow & 12x \color{red}{-2} & = &11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &11+2 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x-7)& = & 11 \color{red}{+} (5+2x) \\\Leftrightarrow & -3x-21& = &11+5+2x \\\Leftrightarrow & -3x \color{red}{-21} & = &16 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & -3x-2x& = &16+21 \\\Leftrightarrow & -5x& = &37 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{37}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-37}{5} & & \\ & V = \left\{ \frac{-37}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-7)& = & -1 \color{red}{+} (7+x) \\\Leftrightarrow & 30x-42& = &-1+7+x \\\Leftrightarrow & 30x \color{red}{-42} & = &6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &6+42 \\\Leftrightarrow & 29x& = &48 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{48}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{48}{29} & & \\ & V = \left\{ \frac{48}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x+1)& = & -2 \color{red}{-} (3-3x) \\\Leftrightarrow & 4x+2& = &-2-3+3x \\\Leftrightarrow & 4x \color{red}{+2} & = &-5 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 4x-3x& = &-5-2 \\\Leftrightarrow & x& = &-7 \\ & V = \left\{ -7 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+7)& = & 4 \color{red}{-} (11+x) \\\Leftrightarrow & 15x+21& = &4-11-x \\\Leftrightarrow & 15x \color{red}{+21} & = &-7 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 15x+x& = &-7-21 \\\Leftrightarrow & 16x& = &-28 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-28}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-7}{4} & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-7)& = & -7 \color{red}{-} (7+x) \\\Leftrightarrow & -10x-14& = &-7-7-x \\\Leftrightarrow & -10x \color{red}{-14} & = &-14 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -10x+x& = &-14+14 \\\Leftrightarrow & -9x& = &0 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{0}{ \color{red}{-9} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+1)& = & -12 \color{red}{-} (-15+x) \\\Leftrightarrow & 4x+4& = &-12+15-x \\\Leftrightarrow & 4x \color{red}{+4} & = &3 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 4x+x& = &3-4 \\\Leftrightarrow & 5x& = &-1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (5x+7)& = & -9 \color{red}{+} (1+x) \\\Leftrightarrow & 10x+14& = &-9+1+x \\\Leftrightarrow & 10x \color{red}{+14} & = &-8 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 10x-x& = &-8-14 \\\Leftrightarrow & 9x& = &-22 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-22}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)