Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-7)& = & -10 \color{red}{-} (2-2x) \\\Leftrightarrow & 3x-21& = &-10-2+2x \\\Leftrightarrow & 3x \color{red}{-21} & = &-12 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & 3x-2x& = &-12+21 \\\Leftrightarrow & x& = &9 \\ & V = \left\{ 9 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+4)& = & -9 \color{red}{-} (9+x) \\\Leftrightarrow & -6x+12& = &-9-9-x \\\Leftrightarrow & -6x \color{red}{+12} & = &-18 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -6x+x& = &-18-12 \\\Leftrightarrow & -5x& = &-30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-30}{ \color{red}{-5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-6)& = & 1 \color{red}{+} (8+x) \\\Leftrightarrow & 24x-36& = &1+8+x \\\Leftrightarrow & 24x \color{red}{-36} & = &9 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 24x-x& = &9+36 \\\Leftrightarrow & 23x& = &45 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{45}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{45}{23} & & \\ & V = \left\{ \frac{45}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x+7)& = & 13 \color{red}{+} (-10-2x) \\\Leftrightarrow & 15x+35& = &13-10-2x \\\Leftrightarrow & 15x \color{red}{+35} & = &3 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-35} \\\Leftrightarrow & 15x+2x& = &3-35 \\\Leftrightarrow & 17x& = &-32 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-32}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-32}{17} & & \\ & V = \left\{ \frac{-32}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x+6)& = & 12 \color{red}{+} (11+3x) \\\Leftrightarrow & -25x+30& = &12+11+3x \\\Leftrightarrow & -25x \color{red}{+30} & = &23 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &23 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & -25x-3x& = &23-30 \\\Leftrightarrow & -28x& = &-7 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-7}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-1)& = & 11 \color{red}{-} (-8-5x) \\\Leftrightarrow & 18x-6& = &11+8+5x \\\Leftrightarrow & 18x \color{red}{-6} & = &19 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 18x-5x& = &19+6 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x-7)& = & 7 \color{red}{-} (13+x) \\\Leftrightarrow & 12x-21& = &7-13-x \\\Leftrightarrow & 12x \color{red}{-21} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 12x+x& = &-6+21 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (x-1)& = & -9 \color{red}{+} (-15-3x) \\\Leftrightarrow & 4x-4& = &-9-15-3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-24 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 4x+3x& = &-24+4 \\\Leftrightarrow & 7x& = &-20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+7)& = & -7 \color{red}{+} (3+x) \\\Leftrightarrow & -36x+42& = &-7+3+x \\\Leftrightarrow & -36x \color{red}{+42} & = &-4 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -36x-x& = &-4-42 \\\Leftrightarrow & -37x& = &-46 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-46}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{46}{37} & & \\ & V = \left\{ \frac{46}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x-7)& = & 2 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x-28& = &2-3+x \\\Leftrightarrow & -20x \color{red}{-28} & = &-1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -20x-x& = &-1+28 \\\Leftrightarrow & -21x& = &27 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{27}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-9}{7} & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x+6)& = & 2 \color{red}{-} (-4+x) \\\Leftrightarrow & -3x+18& = &2+4-x \\\Leftrightarrow & -3x \color{red}{+18} & = &6 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -3x+x& = &6-18 \\\Leftrightarrow & -2x& = &-12 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-12}{ \color{red}{-2} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x+1)& = & 9 \color{red}{+} (13+x) \\\Leftrightarrow & 4x+4& = &9+13+x \\\Leftrightarrow & 4x \color{red}{+4} & = &22 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 4x-x& = &22-4 \\\Leftrightarrow & 3x& = &18 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{18}{ \color{red}{3} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)