Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(-6x-7)=5-(-8-5x)\)
2. \(2(-2x+5)=-12-(2+x)\)
3. \(3(4x-1)=-4+(4+x)\)
4. \(5(5x+7)=2-(-6+4x)\)
5. \(4(4x-1)=-3+(13+3x)\)
6. \(6(2x-5)=-6+(15+x)\)
7. \(6(-2x+2)=12-(13+x)\)
8. \(2(6x+2)=-11-(-10+x)\)
9. \(6(-2x-1)=15-(10+x)\)
10. \(4(-3x+3)=3-(13+x)\)
11. \(4(-5x+4)=-6-(6+x)\)
12. \(2(-4x-1)=-13-(1+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-7)& = & 5 \color{red}{-} (-8-5x) \\\Leftrightarrow & -36x-42& = &5+8+5x \\\Leftrightarrow & -36x \color{red}{-42} & = &13 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & -36x-5x& = &13+42 \\\Leftrightarrow & -41x& = &55 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{55}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-55}{41} & & \\ & V = \left\{ \frac{-55}{41} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+5)& = & -12 \color{red}{-} (2+x) \\\Leftrightarrow & -4x+10& = &-12-2-x \\\Leftrightarrow & -4x \color{red}{+10} & = &-14 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -4x+x& = &-14-10 \\\Leftrightarrow & -3x& = &-24 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-24}{ \color{red}{-3} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-1)& = & -4 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-3& = &-4+4+x \\\Leftrightarrow & 12x \color{red}{-3} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 12x-x& = &0+3 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x+7)& = & 2 \color{red}{-} (-6+4x) \\\Leftrightarrow & 25x+35& = &2+6-4x \\\Leftrightarrow & 25x \color{red}{+35} & = &8 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &8 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & 25x+4x& = &8-35 \\\Leftrightarrow & 29x& = &-27 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-27}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-27}{29} & & \\ & V = \left\{ \frac{-27}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-1)& = & -3 \color{red}{+} (13+3x) \\\Leftrightarrow & 16x-4& = &-3+13+3x \\\Leftrightarrow & 16x \color{red}{-4} & = &10 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 16x-3x& = &10+4 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x-5)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & 12x-30& = &-6+15+x \\\Leftrightarrow & 12x \color{red}{-30} & = &9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &9+30 \\\Leftrightarrow & 11x& = &39 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{39}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{39}{11} & & \\ & V = \left\{ \frac{39}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-2x+2)& = & 12 \color{red}{-} (13+x) \\\Leftrightarrow & -12x+12& = &12-13-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-1-12 \\\Leftrightarrow & -11x& = &-13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (6x+2)& = & -11 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x+4& = &-11+10-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-1-4 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x-1)& = & 15 \color{red}{-} (10+x) \\\Leftrightarrow & -12x-6& = &15-10-x \\\Leftrightarrow & -12x \color{red}{-6} & = &5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &5+6 \\\Leftrightarrow & -11x& = &11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{11}{ \color{red}{-11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x+3)& = & 3 \color{red}{-} (13+x) \\\Leftrightarrow & -12x+12& = &3-13-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-10-12 \\\Leftrightarrow & -11x& = &-22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-22}{ \color{red}{-11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+4)& = & -6 \color{red}{-} (6+x) \\\Leftrightarrow & -20x+16& = &-6-6-x \\\Leftrightarrow & -20x \color{red}{+16} & = &-12 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -20x+x& = &-12-16 \\\Leftrightarrow & -19x& = &-28 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-28}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{28}{19} & & \\ & V = \left\{ \frac{28}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x-1)& = & -13 \color{red}{-} (1+x) \\\Leftrightarrow & -8x-2& = &-13-1-x \\\Leftrightarrow & -8x \color{red}{-2} & = &-14 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -8x+x& = &-14+2 \\\Leftrightarrow & -7x& = &-12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)