Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-7}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7-13x } & = & 3 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+9}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+5x } & = & -15 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &16x & = &-24\\\Leftrightarrow & \color{red}{16}x & = &-24\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-24}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+10}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-7x } & = & -8 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-15}& = & -6 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15+6x } & = & -6 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -6 \color{blue}{+15} \\\Leftrightarrow &19x & = &9\\\Leftrightarrow & \color{red}{19}x & = &9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-2}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-14x } & = & 1 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &-25x & = &3\\\Leftrightarrow & \color{red}{-25}x & = &3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-15}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-x } & = & -3 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+1}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-3x } & = & 5 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+9}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9-13x } & = & -12 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-25x & = &-21\\\Leftrightarrow & \color{red}{-25}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-21}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{21}{25} } & & \\ & V = \left\{ \frac{21}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-10}& = & -3 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10-2x } & = & -3 \color{red}{ +2x }\color{blue}{+10-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-3}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+13x } & = & -1 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &27x & = &2\\\Leftrightarrow & \color{red}{27}x & = &2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{27} } & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+11}& = & -14 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+5x } & = & -14 \color{red}{ -5x }\color{blue}{-11+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &16x & = &-25\\\Leftrightarrow & \color{red}{16}x & = &-25\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-25}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{16} } & & \\ & V = \left\{ \frac{-25}{16} \right\} & \\\end{align}\)