Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x+4)& = & 15 \color{red}{-} (5-5x) \\\Leftrightarrow & -8x+16& = &15-5+5x \\\Leftrightarrow & -8x \color{red}{+16} & = &10 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & -8x-5x& = &10-16 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+3)& = & 7 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x+9& = &7-6+x \\\Leftrightarrow & 6x \color{red}{+9} & = &1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 6x-x& = &1-9 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-2)& = & 12 \color{red}{-} (-9+x) \\\Leftrightarrow & 24x-12& = &12+9-x \\\Leftrightarrow & 24x \color{red}{-12} & = &21 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &21+12 \\\Leftrightarrow & 25x& = &33 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{33}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{33}{25} & & \\ & V = \left\{ \frac{33}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x+6)& = & 2 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+12& = &2+4+x \\\Leftrightarrow & 12x \color{red}{+12} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &6-12 \\\Leftrightarrow & 11x& = &-6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-1)& = & -5 \color{red}{+} (11+x) \\\Leftrightarrow & -30x-5& = &-5+11+x \\\Leftrightarrow & -30x \color{red}{-5} & = &6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &6+5 \\\Leftrightarrow & -31x& = &11 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{11}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-11}{31} & & \\ & V = \left\{ \frac{-11}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-1)& = & 10 \color{red}{+} (-1+x) \\\Leftrightarrow & 18x-3& = &10-1+x \\\Leftrightarrow & 18x \color{red}{-3} & = &9 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 18x-x& = &9+3 \\\Leftrightarrow & 17x& = &12 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{12}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{12}{17} & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+2)& = & -3 \color{red}{-} (10+x) \\\Leftrightarrow & 8x+4& = &-3-10-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-13 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-13-4 \\\Leftrightarrow & 9x& = &-17 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-17}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-17}{9} & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+3)& = & -1 \color{red}{-} (15-2x) \\\Leftrightarrow & -15x+9& = &-1-15+2x \\\Leftrightarrow & -15x \color{red}{+9} & = &-16 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & -15x-2x& = &-16-9 \\\Leftrightarrow & -17x& = &-25 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-25}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{25}{17} & & \\ & V = \left\{ \frac{25}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+5)& = & 10 \color{red}{-} (-3+x) \\\Leftrightarrow & -10x+25& = &10+3-x \\\Leftrightarrow & -10x \color{red}{+25} & = &13 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -10x+x& = &13-25 \\\Leftrightarrow & -9x& = &-12 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-12}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-5x+7)& = & 7 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x+42& = &7+1-x \\\Leftrightarrow & -30x \color{red}{+42} & = &8 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &8-42 \\\Leftrightarrow & -29x& = &-34 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-34}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{34}{29} & & \\ & V = \left\{ \frac{34}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+3)& = & -8 \color{red}{-} (6+x) \\\Leftrightarrow & 20x+15& = &-8-6-x \\\Leftrightarrow & 20x \color{red}{+15} & = &-14 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 20x+x& = &-14-15 \\\Leftrightarrow & 21x& = &-29 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-29}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-29}{21} & & \\ & V = \left\{ \frac{-29}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x+5)& = & -12 \color{red}{+} (12+x) \\\Leftrightarrow & -6x+10& = &-12+12+x \\\Leftrightarrow & -6x \color{red}{+10} & = &0 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -6x-x& = &0-10 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)