Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x-7)& = & 11 \color{red}{-} (5+x) \\\Leftrightarrow & 24x-42& = &11-5-x \\\Leftrightarrow & 24x \color{red}{-42} & = &6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 24x+x& = &6+42 \\\Leftrightarrow & 25x& = &48 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{48}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{48}{25} & & \\ & V = \left\{ \frac{48}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x+5)& = & 13 \color{red}{+} (-6-4x) \\\Leftrightarrow & 9x+15& = &13-6-4x \\\Leftrightarrow & 9x \color{red}{+15} & = &7 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 9x+4x& = &7-15 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+7)& = & -4 \color{red}{-} (11+3x) \\\Leftrightarrow & 8x+14& = &-4-11-3x \\\Leftrightarrow & 8x \color{red}{+14} & = &-15 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &-15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 8x+3x& = &-15-14 \\\Leftrightarrow & 11x& = &-29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x+3)& = & 10 \color{red}{-} (-5+x) \\\Leftrightarrow & 3x+9& = &10+5-x \\\Leftrightarrow & 3x \color{red}{+9} & = &15 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 3x+x& = &15-9 \\\Leftrightarrow & 4x& = &6 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{6}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{3}{2} & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-6x-3)& = & -8 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x-15& = &-8-6+x \\\Leftrightarrow & -30x \color{red}{-15} & = &-14 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &-14+15 \\\Leftrightarrow & -31x& = &1 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{1}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-1}{31} & & \\ & V = \left\{ \frac{-1}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x+7)& = & 8 \color{red}{+} (1+x) \\\Leftrightarrow & -12x+42& = &8+1+x \\\Leftrightarrow & -12x \color{red}{+42} & = &9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -12x-x& = &9-42 \\\Leftrightarrow & -13x& = &-33 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-33}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x-6)& = & 2 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-36& = &2+6+x \\\Leftrightarrow & -12x \color{red}{-36} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -12x-x& = &8+36 \\\Leftrightarrow & -13x& = &44 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{44}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-44}{13} & & \\ & V = \left\{ \frac{-44}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x-1)& = & -5 \color{red}{+} (7+x) \\\Leftrightarrow & 30x-5& = &-5+7+x \\\Leftrightarrow & 30x \color{red}{-5} & = &2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 30x-x& = &2+5 \\\Leftrightarrow & 29x& = &7 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{7}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{7}{29} & & \\ & V = \left\{ \frac{7}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x+5)& = & 9 \color{red}{-} (3+x) \\\Leftrightarrow & 20x+20& = &9-3-x \\\Leftrightarrow & 20x \color{red}{+20} & = &6 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &6-20 \\\Leftrightarrow & 21x& = &-14 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-14}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x+4)& = & -7 \color{red}{+} (-7-5x) \\\Leftrightarrow & -16x+16& = &-7-7-5x \\\Leftrightarrow & -16x \color{red}{+16} & = &-14 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+16} \color{blue}{-16} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-16} \\\Leftrightarrow & -16x+5x& = &-14-16 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x-2)& = & 4 \color{red}{-} (-9+x) \\\Leftrightarrow & -12x-6& = &4+9-x \\\Leftrightarrow & -12x \color{red}{-6} & = &13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &13+6 \\\Leftrightarrow & -11x& = &19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x+1)& = & 10 \color{red}{-} (1-2x) \\\Leftrightarrow & -15x+3& = &10-1+2x \\\Leftrightarrow & -15x \color{red}{+3} & = &9 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -15x-2x& = &9-3 \\\Leftrightarrow & -17x& = &6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)