Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-6)& = & -6 \color{red}{-} (-8+x) \\\Leftrightarrow & 2x-12& = &-6+8-x \\\Leftrightarrow & 2x \color{red}{-12} & = &2 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 2x+x& = &2+12 \\\Leftrightarrow & 3x& = &14 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{14}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{14}{3} & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x+1)& = & -6 \color{red}{+} (7+x) \\\Leftrightarrow & 18x+3& = &-6+7+x \\\Leftrightarrow & 18x \color{red}{+3} & = &1 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 18x-x& = &1-3 \\\Leftrightarrow & 17x& = &-2 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-2}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x+4)& = & 9 \color{red}{+} (12-5x) \\\Leftrightarrow & -6x+8& = &9+12-5x \\\Leftrightarrow & -6x \color{red}{+8} & = &21 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -6x+5x& = &21-8 \\\Leftrightarrow & -x& = &13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{13}{ \color{red}{-1} } \\\Leftrightarrow & x = -13 & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x+6)& = & 15 \color{red}{-} (-7-5x) \\\Leftrightarrow & 8x+12& = &15+7+5x \\\Leftrightarrow & 8x \color{red}{+12} & = &22 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 8x-5x& = &22-12 \\\Leftrightarrow & 3x& = &10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x+5)& = & 2 \color{red}{+} (-8-5x) \\\Leftrightarrow & -8x+20& = &2-8-5x \\\Leftrightarrow & -8x \color{red}{+20} & = &-6 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-20} \\\Leftrightarrow & -8x+5x& = &-6-20 \\\Leftrightarrow & -3x& = &-26 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-26}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{26}{3} & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x-7)& = & -10 \color{red}{+} (-8-5x) \\\Leftrightarrow & -18x-42& = &-10-8-5x \\\Leftrightarrow & -18x \color{red}{-42} & = &-18 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & -18x+5x& = &-18+42 \\\Leftrightarrow & -13x& = &24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x-7)& = & -7 \color{red}{-} (-15-5x) \\\Leftrightarrow & 6x-14& = &-7+15+5x \\\Leftrightarrow & 6x \color{red}{-14} & = &8 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+14} \\\Leftrightarrow & 6x-5x& = &8+14 \\\Leftrightarrow & x& = &22 \\ & V = \left\{ 22 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (5x-7)& = & 6 \color{red}{-} (-13-4x) \\\Leftrightarrow & 25x-35& = &6+13+4x \\\Leftrightarrow & 25x \color{red}{-35} & = &19 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{-4x} & = &19 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+35} \\\Leftrightarrow & 25x-4x& = &19+35 \\\Leftrightarrow & 21x& = &54 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{54}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-6)& = & -10 \color{red}{+} (10-2x) \\\Leftrightarrow & -9x-18& = &-10+10-2x \\\Leftrightarrow & -9x \color{red}{-18} & = &0 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &0 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & -9x+2x& = &0+18 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+1)& = & -8 \color{red}{-} (15+x) \\\Leftrightarrow & -18x+3& = &-8-15-x \\\Leftrightarrow & -18x \color{red}{+3} & = &-23 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -18x+x& = &-23-3 \\\Leftrightarrow & -17x& = &-26 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-26}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{26}{17} & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x-1)& = & 9 \color{red}{+} (-15-5x) \\\Leftrightarrow & 6x-3& = &9-15-5x \\\Leftrightarrow & 6x \color{red}{-3} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & 6x+5x& = &-6+3 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+2)& = & 10 \color{red}{-} (5+x) \\\Leftrightarrow & -30x+10& = &10-5-x \\\Leftrightarrow & -30x \color{red}{+10} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -30x+x& = &5-10 \\\Leftrightarrow & -29x& = &-5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)