Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x+5)& = & -7 \color{red}{+} (-9+x) \\\Leftrightarrow & 8x+20& = &-7-9+x \\\Leftrightarrow & 8x \color{red}{+20} & = &-16 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 8x-x& = &-16-20 \\\Leftrightarrow & 7x& = &-36 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-36}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-36}{7} & & \\ & V = \left\{ \frac{-36}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-3)& = & 4 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-9& = &4-1+x \\\Leftrightarrow & 12x \color{red}{-9} & = &3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 12x-x& = &3+9 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (5x+3)& = & 14 \color{red}{-} (6+x) \\\Leftrightarrow & 30x+18& = &14-6-x \\\Leftrightarrow & 30x \color{red}{+18} & = &8 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &8-18 \\\Leftrightarrow & 31x& = &-10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x-5)& = & -4 \color{red}{+} (2-3x) \\\Leftrightarrow & 4x-10& = &-4+2-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &-2+10 \\\Leftrightarrow & 7x& = &8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x-4)& = & -11 \color{red}{+} (-9+x) \\\Leftrightarrow & -30x-24& = &-11-9+x \\\Leftrightarrow & -30x \color{red}{-24} & = &-20 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -30x-x& = &-20+24 \\\Leftrightarrow & -31x& = &4 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{4}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-4}{31} & & \\ & V = \left\{ \frac{-4}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-1)& = & 2 \color{red}{-} (2-5x) \\\Leftrightarrow & -36x-6& = &2-2+5x \\\Leftrightarrow & -36x \color{red}{-6} & = &0 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -36x-5x& = &0+6 \\\Leftrightarrow & -41x& = &6 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{6}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-6}{41} & & \\ & V = \left\{ \frac{-6}{41} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x+5)& = & -12 \color{red}{-} (-8-5x) \\\Leftrightarrow & -8x+10& = &-12+8+5x \\\Leftrightarrow & -8x \color{red}{+10} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & -8x-5x& = &-4-10 \\\Leftrightarrow & -13x& = &-14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x+1)& = & 5 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x+3& = &5-5+x \\\Leftrightarrow & -12x \color{red}{+3} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &0-3 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x-5)& = & -2 \color{red}{-} (10-5x) \\\Leftrightarrow & 16x-20& = &-2-10+5x \\\Leftrightarrow & 16x \color{red}{-20} & = &-12 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+20} \\\Leftrightarrow & 16x-5x& = &-12+20 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x+3)& = & -2 \color{red}{+} (-11-4x) \\\Leftrightarrow & -25x+15& = &-2-11-4x \\\Leftrightarrow & -25x \color{red}{+15} & = &-13 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -25x+4x& = &-13-15 \\\Leftrightarrow & -21x& = &-28 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-28}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+3)& = & -9 \color{red}{+} (1-5x) \\\Leftrightarrow & 6x+6& = &-9+1-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-8 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &-8-6 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x-2)& = & 7 \color{red}{-} (10+x) \\\Leftrightarrow & 6x-12& = &7-10-x \\\Leftrightarrow & 6x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &-3+12 \\\Leftrightarrow & 7x& = &9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)