Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x-7)& = & -9 \color{red}{-} (9-5x) \\\Leftrightarrow & 18x-42& = &-9-9+5x \\\Leftrightarrow & 18x \color{red}{-42} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 18x-5x& = &-18+42 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-2)& = & 13 \color{red}{-} (8-3x) \\\Leftrightarrow & -4x-8& = &13-8+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &5+8 \\\Leftrightarrow & -7x& = &13 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{13}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-13}{7} & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-3)& = & -7 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x-6& = &-7+5-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-2+6 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+4)& = & 15 \color{red}{+} (15-5x) \\\Leftrightarrow & 36x+24& = &15+15-5x \\\Leftrightarrow & 36x \color{red}{+24} & = &30 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{+5x} & = &30 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-24} \\\Leftrightarrow & 36x+5x& = &30-24 \\\Leftrightarrow & 41x& = &6 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{6}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{6}{41} & & \\ & V = \left\{ \frac{6}{41} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x-6)& = & -9 \color{red}{-} (5+x) \\\Leftrightarrow & -12x-12& = &-9-5-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-14+12 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x-5)& = & -2 \color{red}{-} (1+x) \\\Leftrightarrow & 25x-25& = &-2-1-x \\\Leftrightarrow & 25x \color{red}{-25} & = &-3 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 25x+x& = &-3+25 \\\Leftrightarrow & 26x& = &22 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{22}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-6)& = & -5 \color{red}{+} (-7+3x) \\\Leftrightarrow & -5x-30& = &-5-7+3x \\\Leftrightarrow & -5x \color{red}{-30} & = &-12 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+30} \\\Leftrightarrow & -5x-3x& = &-12+30 \\\Leftrightarrow & -8x& = &18 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{18}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x+1)& = & -4 \color{red}{+} (-13-3x) \\\Leftrightarrow & 4x+2& = &-4-13-3x \\\Leftrightarrow & 4x \color{red}{+2} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & 4x+3x& = &-17-2 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-3)& = & -2 \color{red}{-} (1+x) \\\Leftrightarrow & 18x-18& = &-2-1-x \\\Leftrightarrow & 18x \color{red}{-18} & = &-3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 18x+x& = &-3+18 \\\Leftrightarrow & 19x& = &15 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{15}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{15}{19} & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+2)& = & -4 \color{red}{+} (-3-5x) \\\Leftrightarrow & -8x+8& = &-4-3-5x \\\Leftrightarrow & -8x \color{red}{+8} & = &-7 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -8x+5x& = &-7-8 \\\Leftrightarrow & -3x& = &-15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-15}{ \color{red}{-3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+1)& = & -7 \color{red}{-} (13+x) \\\Leftrightarrow & -12x+6& = &-7-13-x \\\Leftrightarrow & -12x \color{red}{+6} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &-20-6 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x+4)& = & -9 \color{red}{+} (9+x) \\\Leftrightarrow & -9x+12& = &-9+9+x \\\Leftrightarrow & -9x \color{red}{+12} & = &0 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -9x-x& = &0-12 \\\Leftrightarrow & -10x& = &-12 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-12}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)