Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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