Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x-6)& = & -15 \color{red}{-} (11+x) \\\Leftrightarrow & 24x-36& = &-15-11-x \\\Leftrightarrow & 24x \color{red}{-36} & = &-26 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &-26+36 \\\Leftrightarrow & 25x& = &10 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{10}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+2)& = & -10 \color{red}{+} (1+x) \\\Leftrightarrow & -20x+8& = &-10+1+x \\\Leftrightarrow & -20x \color{red}{+8} & = &-9 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &-9-8 \\\Leftrightarrow & -21x& = &-17 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-17}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{17}{21} & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-1)& = & -15 \color{red}{+} (8+x) \\\Leftrightarrow & 4x-4& = &-15+8+x \\\Leftrightarrow & 4x \color{red}{-4} & = &-7 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 4x-x& = &-7+4 \\\Leftrightarrow & 3x& = &-3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-3}{ \color{red}{3} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x-7)& = & 4 \color{red}{-} (2+x) \\\Leftrightarrow & -12x-14& = &4-2-x \\\Leftrightarrow & -12x \color{red}{-14} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -12x+x& = &2+14 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x+5)& = & -8 \color{red}{-} (8-3x) \\\Leftrightarrow & 10x+10& = &-8-8+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &-16-10 \\\Leftrightarrow & 7x& = &-26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-26}{7} & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x-7)& = & 11 \color{red}{-} (-8-5x) \\\Leftrightarrow & 36x-42& = &11+8+5x \\\Leftrightarrow & 36x \color{red}{-42} & = &19 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & 36x-5x& = &19+42 \\\Leftrightarrow & 31x& = &61 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{61}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{61}{31} & & \\ & V = \left\{ \frac{61}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-1)& = & -11 \color{red}{-} (-9+x) \\\Leftrightarrow & -15x-3& = &-11+9-x \\\Leftrightarrow & -15x \color{red}{-3} & = &-2 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -15x+x& = &-2+3 \\\Leftrightarrow & -14x& = &1 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{1}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-1}{14} & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x-1)& = & 7 \color{red}{+} (-10+3x) \\\Leftrightarrow & -10x-5& = &7-10+3x \\\Leftrightarrow & -10x \color{red}{-5} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-5} \color{blue}{+5} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+5} \\\Leftrightarrow & -10x-3x& = &-3+5 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x+7)& = & 3 \color{red}{-} (15+3x) \\\Leftrightarrow & 10x+35& = &3-15-3x \\\Leftrightarrow & 10x \color{red}{+35} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 10x+3x& = &-12-35 \\\Leftrightarrow & 13x& = &-47 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-47}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-47}{13} & & \\ & V = \left\{ \frac{-47}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x+1)& = & 14 \color{red}{+} (-12-5x) \\\Leftrightarrow & -6x+6& = &14-12-5x \\\Leftrightarrow & -6x \color{red}{+6} & = &2 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -6x+5x& = &2-6 \\\Leftrightarrow & -x& = &-4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-4}{ \color{red}{-1} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+2)& = & 3 \color{red}{-} (-15-5x) \\\Leftrightarrow & 6x+6& = &3+15+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &18 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &18-6 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+1)& = & -14 \color{red}{-} (5+x) \\\Leftrightarrow & 20x+4& = &-14-5-x \\\Leftrightarrow & 20x \color{red}{+4} & = &-19 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 20x+x& = &-19-4 \\\Leftrightarrow & 21x& = &-23 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-23}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-23}{21} & & \\ & V = \left\{ \frac{-23}{21} \right\} & \\\end{align}\)