Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x+3)& = & -2 \color{red}{-} (4-5x) \\\Leftrightarrow & 3x+9& = &-2-4+5x \\\Leftrightarrow & 3x \color{red}{+9} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 3x-5x& = &-6-9 \\\Leftrightarrow & -2x& = &-15 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-15}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{15}{2} & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x-4)& = & -5 \color{red}{+} (6+3x) \\\Leftrightarrow & 16x-16& = &-5+6+3x \\\Leftrightarrow & 16x \color{red}{-16} & = &1 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & 16x-3x& = &1+16 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-5)& = & 1 \color{red}{-} (8+x) \\\Leftrightarrow & 15x-25& = &1-8-x \\\Leftrightarrow & 15x \color{red}{-25} & = &-7 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 15x+x& = &-7+25 \\\Leftrightarrow & 16x& = &18 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{18}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{9}{8} & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (4x-1)& = & 10 \color{red}{-} (-4+3x) \\\Leftrightarrow & 16x-4& = &10+4-3x \\\Leftrightarrow & 16x \color{red}{-4} & = &14 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 16x+3x& = &14+4 \\\Leftrightarrow & 19x& = &18 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{18}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{18}{19} & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-2x-4)& = & 4 \color{red}{-} (-6-3x) \\\Leftrightarrow & -4x-8& = &4+6+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &10 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &10+8 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-5x+7)& = & -10 \color{red}{-} (-7+4x) \\\Leftrightarrow & -15x+21& = &-10+7-4x \\\Leftrightarrow & -15x \color{red}{+21} & = &-3 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -15x+4x& = &-3-21 \\\Leftrightarrow & -11x& = &-24 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-24}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{24}{11} & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-3x+2)& = & 2 \color{red}{-} (9+x) \\\Leftrightarrow & -12x+8& = &2-9-x \\\Leftrightarrow & -12x \color{red}{+8} & = &-7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &-7-8 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+2)& = & 8 \color{red}{+} (5+x) \\\Leftrightarrow & -8x+4& = &8+5+x \\\Leftrightarrow & -8x \color{red}{+4} & = &13 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -8x-x& = &13-4 \\\Leftrightarrow & -9x& = &9 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{9}{ \color{red}{-9} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+7)& = & 6 \color{red}{-} (12+x) \\\Leftrightarrow & 24x+42& = &6-12-x \\\Leftrightarrow & 24x \color{red}{+42} & = &-6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &-6-42 \\\Leftrightarrow & 25x& = &-48 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-48}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-48}{25} & & \\ & V = \left\{ \frac{-48}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x+5)& = & 7 \color{red}{+} (15-4x) \\\Leftrightarrow & 25x+25& = &7+15-4x \\\Leftrightarrow & 25x \color{red}{+25} & = &22 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{+4x} & = &22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-25} \\\Leftrightarrow & 25x+4x& = &22-25 \\\Leftrightarrow & 29x& = &-3 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-3}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-6)& = & 1 \color{red}{-} (-2+x) \\\Leftrightarrow & 20x-30& = &1+2-x \\\Leftrightarrow & 20x \color{red}{-30} & = &3 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 20x+x& = &3+30 \\\Leftrightarrow & 21x& = &33 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{33}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x-6)& = & -9 \color{red}{+} (-12+x) \\\Leftrightarrow & -8x-24& = &-9-12+x \\\Leftrightarrow & -8x \color{red}{-24} & = &-21 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -8x-x& = &-21+24 \\\Leftrightarrow & -9x& = &3 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{3}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)