Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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