Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x-7)& = & -6 \color{red}{+} (7-3x) \\\Leftrightarrow & 4x-28& = &-6+7-3x \\\Leftrightarrow & 4x \color{red}{-28} & = &1 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & 4x+3x& = &1+28 \\\Leftrightarrow & 7x& = &29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{29}{7} & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x+1)& = & 5 \color{red}{+} (14+x) \\\Leftrightarrow & 16x+4& = &5+14+x \\\Leftrightarrow & 16x \color{red}{+4} & = &19 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 16x-x& = &19-4 \\\Leftrightarrow & 15x& = &15 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{15}{ \color{red}{15} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+3)& = & 14 \color{red}{-} (14+x) \\\Leftrightarrow & -8x+12& = &14-14-x \\\Leftrightarrow & -8x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &0-12 \\\Leftrightarrow & -7x& = &-12 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-12}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{12}{7} & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x-1)& = & 8 \color{red}{+} (-9+x) \\\Leftrightarrow & 15x-3& = &8-9+x \\\Leftrightarrow & 15x \color{red}{-3} & = &-1 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 15x-x& = &-1+3 \\\Leftrightarrow & 14x& = &2 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{2}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-5x-3)& = & -8 \color{red}{-} (15-2x) \\\Leftrightarrow & -15x-9& = &-8-15+2x \\\Leftrightarrow & -15x \color{red}{-9} & = &-23 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &-23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -15x-2x& = &-23+9 \\\Leftrightarrow & -17x& = &-14 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-14}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{14}{17} & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-5x-2)& = & 3 \color{red}{-} (-14+3x) \\\Leftrightarrow & -20x-8& = &3+14-3x \\\Leftrightarrow & -20x \color{red}{-8} & = &17 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -20x+3x& = &17+8 \\\Leftrightarrow & -17x& = &25 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{25}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-25}{17} & & \\ & V = \left\{ \frac{-25}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x-5)& = & 9 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x-30& = &9+6-x \\\Leftrightarrow & -24x \color{red}{-30} & = &15 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -24x+x& = &15+30 \\\Leftrightarrow & -23x& = &45 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{45}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-45}{23} & & \\ & V = \left\{ \frac{-45}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x-4)& = & 5 \color{red}{-} (-10+x) \\\Leftrightarrow & 2x-8& = &5+10-x \\\Leftrightarrow & 2x \color{red}{-8} & = &15 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 2x+x& = &15+8 \\\Leftrightarrow & 3x& = &23 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{23}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{23}{3} & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x+4)& = & -7 \color{red}{-} (-11+x) \\\Leftrightarrow & 15x+20& = &-7+11-x \\\Leftrightarrow & 15x \color{red}{+20} & = &4 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 15x+x& = &4-20 \\\Leftrightarrow & 16x& = &-16 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-16}{ \color{red}{16} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-4)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & 10x-20& = &-5-6+x \\\Leftrightarrow & 10x \color{red}{-20} & = &-11 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 10x-x& = &-11+20 \\\Leftrightarrow & 9x& = &9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{9}{ \color{red}{9} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x+2)& = & 9 \color{red}{+} (-6+4x) \\\Leftrightarrow & -3x+6& = &9-6+4x \\\Leftrightarrow & -3x \color{red}{+6} & = &3 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-6} \\\Leftrightarrow & -3x-4x& = &3-6 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+1)& = & 10 \color{red}{-} (-13+x) \\\Leftrightarrow & 12x+6& = &10+13-x \\\Leftrightarrow & 12x \color{red}{+6} & = &23 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &23-6 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)