Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(-4x-1)=9-(-5+x)\)
2. \(2(5x+6)=-13-(6-3x)\)
3. \(6(-2x+7)=15-(14+x)\)
4. \(4(-x+2)=-13-(6+3x)\)
5. \(6(-4x+5)=-1-(6+x)\)
6. \(5(-6x-7)=-6-(-6+x)\)
7. \(4(5x+1)=-2-(15+x)\)
8. \(6(x-2)=-8+(-7+x)\)
9. \(4(2x-2)=9+(13+x)\)
10. \(2(-6x+3)=-3+(-4+x)\)
11. \(3(-3x-2)=-7+(1-4x)\)
12. \(2(-5x+4)=-9+(-8+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-4x-1)& = & 9 \color{red}{-} (-5+x) \\\Leftrightarrow & -24x-6& = &9+5-x \\\Leftrightarrow & -24x \color{red}{-6} & = &14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -24x+x& = &14+6 \\\Leftrightarrow & -23x& = &20 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{20}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-20}{23} & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+6)& = & -13 \color{red}{-} (6-3x) \\\Leftrightarrow & 10x+12& = &-13-6+3x \\\Leftrightarrow & 10x \color{red}{+12} & = &-19 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 10x-3x& = &-19-12 \\\Leftrightarrow & 7x& = &-31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x+7)& = & 15 \color{red}{-} (14+x) \\\Leftrightarrow & -12x+42& = &15-14-x \\\Leftrightarrow & -12x \color{red}{+42} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &1-42 \\\Leftrightarrow & -11x& = &-41 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-41}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{41}{11} & & \\ & V = \left\{ \frac{41}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x+2)& = & -13 \color{red}{-} (6+3x) \\\Leftrightarrow & -4x+8& = &-13-6-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &-19 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &-19-8 \\\Leftrightarrow & -x& = &-27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-27}{ \color{red}{-1} } \\\Leftrightarrow & x = 27 & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x+5)& = & -1 \color{red}{-} (6+x) \\\Leftrightarrow & -24x+30& = &-1-6-x \\\Leftrightarrow & -24x \color{red}{+30} & = &-7 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -24x+x& = &-7-30 \\\Leftrightarrow & -23x& = &-37 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-37}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{37}{23} & & \\ & V = \left\{ \frac{37}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-7)& = & -6 \color{red}{-} (-6+x) \\\Leftrightarrow & -30x-35& = &-6+6-x \\\Leftrightarrow & -30x \color{red}{-35} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -30x+x& = &0+35 \\\Leftrightarrow & -29x& = &35 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{35}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-35}{29} & & \\ & V = \left\{ \frac{-35}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x+1)& = & -2 \color{red}{-} (15+x) \\\Leftrightarrow & 20x+4& = &-2-15-x \\\Leftrightarrow & 20x \color{red}{+4} & = &-17 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 20x+x& = &-17-4 \\\Leftrightarrow & 21x& = &-21 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-21}{ \color{red}{21} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x-2)& = & -8 \color{red}{+} (-7+x) \\\Leftrightarrow & 6x-12& = &-8-7+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-15 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-15+12 \\\Leftrightarrow & 5x& = &-3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x-2)& = & 9 \color{red}{+} (13+x) \\\Leftrightarrow & 8x-8& = &9+13+x \\\Leftrightarrow & 8x \color{red}{-8} & = &22 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 8x-x& = &22+8 \\\Leftrightarrow & 7x& = &30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{30}{7} & & \\ & V = \left\{ \frac{30}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x+3)& = & -3 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+6& = &-3-4+x \\\Leftrightarrow & -12x \color{red}{+6} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &-7-6 \\\Leftrightarrow & -13x& = &-13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-13}{ \color{red}{-13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x-2)& = & -7 \color{red}{+} (1-4x) \\\Leftrightarrow & -9x-6& = &-7+1-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &-6 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &-6+6 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+4)& = & -9 \color{red}{+} (-8+x) \\\Leftrightarrow & -10x+8& = &-9-8+x \\\Leftrightarrow & -10x \color{red}{+8} & = &-17 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -10x-x& = &-17-8 \\\Leftrightarrow & -11x& = &-25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)