Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+2)& = & 7 \color{red}{+} (2+x) \\\Leftrightarrow & -30x+12& = &7+2+x \\\Leftrightarrow & -30x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -30x-x& = &9-12 \\\Leftrightarrow & -31x& = &-3 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-3}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x-5)& = & -10 \color{red}{+} (-7+x) \\\Leftrightarrow & -18x-30& = &-10-7+x \\\Leftrightarrow & -18x \color{red}{-30} & = &-17 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -18x-x& = &-17+30 \\\Leftrightarrow & -19x& = &13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x-3)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & 20x-12& = &12-5-x \\\Leftrightarrow & 20x \color{red}{-12} & = &7 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 20x+x& = &7+12 \\\Leftrightarrow & 21x& = &19 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{19}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x-7)& = & 11 \color{red}{+} (7+x) \\\Leftrightarrow & -36x-42& = &11+7+x \\\Leftrightarrow & -36x \color{red}{-42} & = &18 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -36x-x& = &18+42 \\\Leftrightarrow & -37x& = &60 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{60}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-60}{37} & & \\ & V = \left\{ \frac{-60}{37} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x-6)& = & 13 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x-18& = &13-15-5x \\\Leftrightarrow & -6x \color{red}{-18} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -6x+5x& = &-2+18 \\\Leftrightarrow & -x& = &16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{16}{ \color{red}{-1} } \\\Leftrightarrow & x = -16 & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+2)& = & -6 \color{red}{+} (13+x) \\\Leftrightarrow & 8x+8& = &-6+13+x \\\Leftrightarrow & 8x \color{red}{+8} & = &7 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 8x-x& = &7-8 \\\Leftrightarrow & 7x& = &-1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x-6)& = & -14 \color{red}{-} (-9+x) \\\Leftrightarrow & -3x-18& = &-14+9-x \\\Leftrightarrow & -3x \color{red}{-18} & = &-5 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -3x+x& = &-5+18 \\\Leftrightarrow & -2x& = &13 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{13}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-13}{2} & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x+6)& = & 10 \color{red}{-} (-8-5x) \\\Leftrightarrow & -18x+18& = &10+8+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &18 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &18-18 \\\Leftrightarrow & -23x& = &0 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{0}{ \color{red}{-23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-5)& = & 12 \color{red}{-} (5-3x) \\\Leftrightarrow & -4x-20& = &12-5+3x \\\Leftrightarrow & -4x \color{red}{-20} & = &7 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -4x-3x& = &7+20 \\\Leftrightarrow & -7x& = &27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x+7)& = & 5 \color{red}{+} (-14+x) \\\Leftrightarrow & 20x+35& = &5-14+x \\\Leftrightarrow & 20x \color{red}{+35} & = &-9 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 20x-x& = &-9-35 \\\Leftrightarrow & 19x& = &-44 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-44}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-44}{19} & & \\ & V = \left\{ \frac{-44}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x+2)& = & -14 \color{red}{+} (13+x) \\\Leftrightarrow & -6x+12& = &-14+13+x \\\Leftrightarrow & -6x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -6x-x& = &-1-12 \\\Leftrightarrow & -7x& = &-13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x+1)& = & -9 \color{red}{-} (-5+x) \\\Leftrightarrow & 8x+4& = &-9+5-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-4 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-4-4 \\\Leftrightarrow & 9x& = &-8 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-8}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)