Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+2}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-14x } & = & -10 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-27x & = &-12\\\Leftrightarrow & \color{red}{-27}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-12}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+12}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-11x } & = & -15 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-27\\\Leftrightarrow & \color{red}{-3}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-27}{-3} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-12}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+5x } & = & -1 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &8x & = &11\\\Leftrightarrow & \color{red}{8}x & = &11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+7}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-5x } & = & -15 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+2}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-11x } & = & -5 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & -4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+11}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+7x } & = & 13 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+11}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-7x } & = & -6 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-17\\\Leftrightarrow & \color{red}{-16}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+3}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x } & = & 13 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-15x & = &10\\\Leftrightarrow & \color{red}{-15}x & = &10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-11}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-7x } & = & 5 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)