Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(3(-6x+6)=12-(8-5x)\)
2. \(5(2x+7)=-15+(14-3x)\)
3. \(4(x-4)=-5+(12-3x)\)
4. \(2(x-5)=-10-(-4+3x)\)
5. \(5(-5x-6)=-2+(-6+x)\)
6. \(4(2x-4)=-10-(-12+x)\)
7. \(3(6x-4)=-14-(5-5x)\)
8. \(2(x+2)=-4-(9+x)\)
9. \(6(5x+7)=-8+(1+x)\)
10. \(3(-6x+7)=-1-(10+x)\)
11. \(2(5x-1)=2-(9+x)\)
12. \(2(6x-1)=7+(-9+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+6)& = & 12 \color{red}{-} (8-5x) \\\Leftrightarrow & -18x+18& = &12-8+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &4 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &4-18 \\\Leftrightarrow & -23x& = &-14 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-14}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{14}{23} & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x+7)& = & -15 \color{red}{+} (14-3x) \\\Leftrightarrow & 10x+35& = &-15+14-3x \\\Leftrightarrow & 10x \color{red}{+35} & = &-1 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &-1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 10x+3x& = &-1-35 \\\Leftrightarrow & 13x& = &-36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-4)& = & -5 \color{red}{+} (12-3x) \\\Leftrightarrow & 4x-16& = &-5+12-3x \\\Leftrightarrow & 4x \color{red}{-16} & = &7 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 4x+3x& = &7+16 \\\Leftrightarrow & 7x& = &23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-5)& = & -10 \color{red}{-} (-4+3x) \\\Leftrightarrow & 2x-10& = &-10+4-3x \\\Leftrightarrow & 2x \color{red}{-10} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 2x+3x& = &-6+10 \\\Leftrightarrow & 5x& = &4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-6)& = & -2 \color{red}{+} (-6+x) \\\Leftrightarrow & -25x-30& = &-2-6+x \\\Leftrightarrow & -25x \color{red}{-30} & = &-8 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -25x-x& = &-8+30 \\\Leftrightarrow & -26x& = &22 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{22}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x-4)& = & -10 \color{red}{-} (-12+x) \\\Leftrightarrow & 8x-16& = &-10+12-x \\\Leftrightarrow & 8x \color{red}{-16} & = &2 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 8x+x& = &2+16 \\\Leftrightarrow & 9x& = &18 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{18}{ \color{red}{9} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-4)& = & -14 \color{red}{-} (5-5x) \\\Leftrightarrow & 18x-12& = &-14-5+5x \\\Leftrightarrow & 18x \color{red}{-12} & = &-19 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 18x-5x& = &-19+12 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+2)& = & -4 \color{red}{-} (9+x) \\\Leftrightarrow & 2x+4& = &-4-9-x \\\Leftrightarrow & 2x \color{red}{+4} & = &-13 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &-13-4 \\\Leftrightarrow & 3x& = &-17 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-17}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-17}{3} & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+7)& = & -8 \color{red}{+} (1+x) \\\Leftrightarrow & 30x+42& = &-8+1+x \\\Leftrightarrow & 30x \color{red}{+42} & = &-7 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &-7-42 \\\Leftrightarrow & 29x& = &-49 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-49}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-49}{29} & & \\ & V = \left\{ \frac{-49}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+7)& = & -1 \color{red}{-} (10+x) \\\Leftrightarrow & -18x+21& = &-1-10-x \\\Leftrightarrow & -18x \color{red}{+21} & = &-11 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -18x+x& = &-11-21 \\\Leftrightarrow & -17x& = &-32 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-32}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{32}{17} & & \\ & V = \left\{ \frac{32}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x-1)& = & 2 \color{red}{-} (9+x) \\\Leftrightarrow & 10x-2& = &2-9-x \\\Leftrightarrow & 10x \color{red}{-2} & = &-7 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 10x+x& = &-7+2 \\\Leftrightarrow & 11x& = &-5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x-1)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x-2& = &7-9+x \\\Leftrightarrow & 12x \color{red}{-2} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &-2+2 \\\Leftrightarrow & 11x& = &0 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{0}{ \color{red}{11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)