Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+3}& = & 3 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-14x } & = & 3 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-x } & = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &11x & = &26\\\Leftrightarrow & \color{red}{11}x & = &26\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{26}{11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-5}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5-7x } & = & 11 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &3x & = &16\\\Leftrightarrow & \color{red}{3}x & = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & -8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+6}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-13x } & = & -9 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+5}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5-7x } & = & 2 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-x } & = & -10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &7x & = &-23\\\Leftrightarrow & \color{red}{7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-12}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-3x } & = & 3 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+15}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15+13x } & = & -11 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &20x & = &-26\\\Leftrightarrow & \color{red}{20}x & = &-26\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-26}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+8}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-13x } & = & 11 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-19x & = &3\\\Leftrightarrow & \color{red}{-19}x & = &3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-10}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-9x } & = & 15 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-22x & = &25\\\Leftrightarrow & \color{red}{-22}x & = &25\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{25}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{22} } & & \\ & V = \left\{ \frac{-25}{22} \right\} & \\\end{align}\)