Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & -14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-28\\\Leftrightarrow & \color{red}{-13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-28}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{28}{13} } & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+7}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7-5x } & = & 6 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-9}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-3x } & = & 1 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+3}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3+3x } & = & 12 \color{red}{ -3x }\color{blue}{-3+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &10x & = &9\\\Leftrightarrow & \color{red}{10}x & = &9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-4}& = & -5 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+9x } & = & -5 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+15}& = & 14 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-10x } & = & 14 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+6}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-13x } & = & -12 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-7}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+7x } & = & -8 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &12x & = &-1\\\Leftrightarrow & \color{red}{12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & -13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-17\\\Leftrightarrow & \color{red}{-12}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)