Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-13}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-13x } & = & -4 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-28x & = &9\\\Leftrightarrow & \color{red}{-28}x & = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-9}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-5x } & = & -5 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-2}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-11x } & = & 10 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+5}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-7x } & = & 5 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-4}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+11x } & = & -5 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+7}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-11x } & = & 3 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-21x & = &-4\\\Leftrightarrow & \color{red}{-21}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-4}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{21} } & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-6}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-14x } & = & -1 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-23x & = &5\\\Leftrightarrow & \color{red}{-23}x & = &5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-5}& = & 14 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+6x } & = & 14 \color{red}{ -6x }\color{blue}{+5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+13}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-11x } & = & -2 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-x } & = & -1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &4x & = &13\\\Leftrightarrow & \color{red}{4}x & = &13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)