Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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