Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-x } & = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &3x & = &16\\\Leftrightarrow & \color{red}{3}x & = &16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+4}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+11x } & = & -7 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &23x & = &-11\\\Leftrightarrow & \color{red}{23}x & = &-11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-13}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-3x } & = & -2 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+8}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+13x } & = & -14 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &21x & = &-22\\\Leftrightarrow & \color{red}{21}x & = &-22\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-22}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{21} } & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-4}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+11x } & = & 3 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+9}& = & 11 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-2x } & = & 11 \color{red}{ +2x }\color{blue}{-9-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+9}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-5x } & = & 13 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+10}& = & -5 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10-8x } & = & -5 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)