Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x+4)& = & 11 \color{red}{-} (1+x) \\\Leftrightarrow & -18x+24& = &11-1-x \\\Leftrightarrow & -18x \color{red}{+24} & = &10 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -18x+x& = &10-24 \\\Leftrightarrow & -17x& = &-14 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-14}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{14}{17} & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x+5)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x+20& = &-7-8+x \\\Leftrightarrow & -12x \color{red}{+20} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -12x-x& = &-15-20 \\\Leftrightarrow & -13x& = &-35 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-35}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x-6)& = & -11 \color{red}{+} (-6-3x) \\\Leftrightarrow & 10x-30& = &-11-6-3x \\\Leftrightarrow & 10x \color{red}{-30} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & 10x+3x& = &-17+30 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x-1)& = & -2 \color{red}{+} (8+x) \\\Leftrightarrow & 24x-6& = &-2+8+x \\\Leftrightarrow & 24x \color{red}{-6} & = &6 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 24x-x& = &6+6 \\\Leftrightarrow & 23x& = &12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x-2)& = & -3 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x-12& = &-3-9+x \\\Leftrightarrow & 24x \color{red}{-12} & = &-12 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &-12+12 \\\Leftrightarrow & 23x& = &0 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{0}{ \color{red}{23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (4x-6)& = & -2 \color{red}{-} (7-5x) \\\Leftrightarrow & 8x-12& = &-2-7+5x \\\Leftrightarrow & 8x \color{red}{-12} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 8x-5x& = &-9+12 \\\Leftrightarrow & 3x& = &3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{3}{ \color{red}{3} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-3)& = & -14 \color{red}{+} (-13-2x) \\\Leftrightarrow & -15x-9& = &-14-13-2x \\\Leftrightarrow & -15x \color{red}{-9} & = &-27 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &-27 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & -15x+2x& = &-27+9 \\\Leftrightarrow & -13x& = &-18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-4)& = & -10 \color{red}{+} (-8+x) \\\Leftrightarrow & 24x-24& = &-10-8+x \\\Leftrightarrow & 24x \color{red}{-24} & = &-18 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &-18+24 \\\Leftrightarrow & 23x& = &6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x-1)& = & 1 \color{red}{-} (6-5x) \\\Leftrightarrow & 6x-2& = &1-6+5x \\\Leftrightarrow & 6x \color{red}{-2} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & 6x-5x& = &-5+2 \\\Leftrightarrow & x& = &-3 \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x-7)& = & 7 \color{red}{+} (5+3x) \\\Leftrightarrow & -2x-14& = &7+5+3x \\\Leftrightarrow & -2x \color{red}{-14} & = &12 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -2x-3x& = &12+14 \\\Leftrightarrow & -5x& = &26 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{26}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-26}{5} & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x+1)& = & -8 \color{red}{-} (-1+x) \\\Leftrightarrow & -2x+2& = &-8+1-x \\\Leftrightarrow & -2x \color{red}{+2} & = &-7 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -2x+x& = &-7-2 \\\Leftrightarrow & -x& = &-9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-9}{ \color{red}{-1} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x-7)& = & -15 \color{red}{-} (10+4x) \\\Leftrightarrow & 3x-21& = &-15-10-4x \\\Leftrightarrow & 3x \color{red}{-21} & = &-25 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{+4x} & = &-25 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+21} \\\Leftrightarrow & 3x+4x& = &-25+21 \\\Leftrightarrow & 7x& = &-4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)