Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x+7)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & 6x+42& = &7-9+x \\\Leftrightarrow & 6x \color{red}{+42} & = &-2 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 6x-x& = &-2-42 \\\Leftrightarrow & 5x& = &-44 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-44}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-44}{5} & & \\ & V = \left\{ \frac{-44}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x-2)& = & 9 \color{red}{+} (-4+x) \\\Leftrightarrow & 6x-12& = &9-4+x \\\Leftrightarrow & 6x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &5+12 \\\Leftrightarrow & 5x& = &17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-5)& = & -10 \color{red}{-} (6+x) \\\Leftrightarrow & 24x-30& = &-10-6-x \\\Leftrightarrow & 24x \color{red}{-30} & = &-16 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &-16+30 \\\Leftrightarrow & 25x& = &14 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{14}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-x-6)& = & -9 \color{red}{-} (-9-5x) \\\Leftrightarrow & -3x-18& = &-9+9+5x \\\Leftrightarrow & -3x \color{red}{-18} & = &0 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -3x-5x& = &0+18 \\\Leftrightarrow & -8x& = &18 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{18}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-2)& = & -1 \color{red}{+} (-3+x) \\\Leftrightarrow & 30x-12& = &-1-3+x \\\Leftrightarrow & 30x \color{red}{-12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 30x-x& = &-4+12 \\\Leftrightarrow & 29x& = &8 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{8}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{8}{29} & & \\ & V = \left\{ \frac{8}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-3x-5)& = & 15 \color{red}{-} (6+x) \\\Leftrightarrow & -6x-10& = &15-6-x \\\Leftrightarrow & -6x \color{red}{-10} & = &9 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -6x+x& = &9+10 \\\Leftrightarrow & -5x& = &19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-19}{5} & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-2)& = & -6 \color{red}{+} (-12+x) \\\Leftrightarrow & -24x-8& = &-6-12+x \\\Leftrightarrow & -24x \color{red}{-8} & = &-18 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &-18+8 \\\Leftrightarrow & -25x& = &-10 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-10}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x+1)& = & 2 \color{red}{-} (13+x) \\\Leftrightarrow & 30x+6& = &2-13-x \\\Leftrightarrow & 30x \color{red}{+6} & = &-11 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 30x+x& = &-11-6 \\\Leftrightarrow & 31x& = &-17 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-17}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-17}{31} & & \\ & V = \left\{ \frac{-17}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x-6)& = & -10 \color{red}{-} (-8+3x) \\\Leftrightarrow & 4x-24& = &-10+8-3x \\\Leftrightarrow & 4x \color{red}{-24} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & 4x+3x& = &-2+24 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+1)& = & -7 \color{red}{-} (-8+x) \\\Leftrightarrow & -16x+4& = &-7+8-x \\\Leftrightarrow & -16x \color{red}{+4} & = &1 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -16x+x& = &1-4 \\\Leftrightarrow & -15x& = &-3 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-3}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x+6)& = & 4 \color{red}{+} (12+x) \\\Leftrightarrow & -18x+18& = &4+12+x \\\Leftrightarrow & -18x \color{red}{+18} & = &16 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -18x-x& = &16-18 \\\Leftrightarrow & -19x& = &-2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{2}{19} & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x-5)& = & -12 \color{red}{-} (-5+4x) \\\Leftrightarrow & -15x-25& = &-12+5-4x \\\Leftrightarrow & -15x \color{red}{-25} & = &-7 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & -15x+4x& = &-7+25 \\\Leftrightarrow & -11x& = &18 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{18}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)