Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(2x-6)=-9+(4+x)\)
2. \(4(-x+4)=5-(6+x)\)
3. \(2(2x-5)=2-(3-3x)\)
4. \(6(3x+1)=2-(-10-5x)\)
5. \(5(2x-2)=7-(-14-3x)\)
6. \(6(-5x+7)=10-(3+x)\)
7. \(2(3x+2)=10+(7-5x)\)
8. \(2(-6x+3)=-5+(-1+x)\)
9. \(6(-6x-4)=-1-(5-5x)\)
10. \(3(-x-7)=-4+(8+x)\)
11. \(2(6x+2)=10-(-10+x)\)
12. \(2(3x-2)=-7+(-5+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x-6)& = & -9 \color{red}{+} (4+x) \\\Leftrightarrow & 4x-12& = &-9+4+x \\\Leftrightarrow & 4x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 4x-x& = &-5+12 \\\Leftrightarrow & 3x& = &7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+4)& = & 5 \color{red}{-} (6+x) \\\Leftrightarrow & -4x+16& = &5-6-x \\\Leftrightarrow & -4x \color{red}{+16} & = &-1 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -4x+x& = &-1-16 \\\Leftrightarrow & -3x& = &-17 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-17}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{17}{3} & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-5)& = & 2 \color{red}{-} (3-3x) \\\Leftrightarrow & 4x-10& = &2-3+3x \\\Leftrightarrow & 4x \color{red}{-10} & = &-1 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 4x-3x& = &-1+10 \\\Leftrightarrow & x& = &9 \\ & V = \left\{ 9 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x+1)& = & 2 \color{red}{-} (-10-5x) \\\Leftrightarrow & 18x+6& = &2+10+5x \\\Leftrightarrow & 18x \color{red}{+6} & = &12 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 18x-5x& = &12-6 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x-2)& = & 7 \color{red}{-} (-14-3x) \\\Leftrightarrow & 10x-10& = &7+14+3x \\\Leftrightarrow & 10x \color{red}{-10} & = &21 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 10x-3x& = &21+10 \\\Leftrightarrow & 7x& = &31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x+7)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & -30x+42& = &10-3-x \\\Leftrightarrow & -30x \color{red}{+42} & = &7 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &7-42 \\\Leftrightarrow & -29x& = &-35 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-35}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{35}{29} & & \\ & V = \left\{ \frac{35}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x+2)& = & 10 \color{red}{+} (7-5x) \\\Leftrightarrow & 6x+4& = &10+7-5x \\\Leftrightarrow & 6x \color{red}{+4} & = &17 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & 6x+5x& = &17-4 \\\Leftrightarrow & 11x& = &13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+3)& = & -5 \color{red}{+} (-1+x) \\\Leftrightarrow & -12x+6& = &-5-1+x \\\Leftrightarrow & -12x \color{red}{+6} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &-6-6 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x-4)& = & -1 \color{red}{-} (5-5x) \\\Leftrightarrow & -36x-24& = &-1-5+5x \\\Leftrightarrow & -36x \color{red}{-24} & = &-6 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & -36x-5x& = &-6+24 \\\Leftrightarrow & -41x& = &18 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{18}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-18}{41} & & \\ & V = \left\{ \frac{-18}{41} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x-7)& = & -4 \color{red}{+} (8+x) \\\Leftrightarrow & -3x-21& = &-4+8+x \\\Leftrightarrow & -3x \color{red}{-21} & = &4 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -3x-x& = &4+21 \\\Leftrightarrow & -4x& = &25 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{25}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-25}{4} & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x+2)& = & 10 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x+4& = &10+10-x \\\Leftrightarrow & 12x \color{red}{+4} & = &20 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &20-4 \\\Leftrightarrow & 13x& = &16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x-2)& = & -7 \color{red}{+} (-5+x) \\\Leftrightarrow & 6x-4& = &-7-5+x \\\Leftrightarrow & 6x \color{red}{-4} & = &-12 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 6x-x& = &-12+4 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)