Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+14}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-13x } & = & 13 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-13}& = & 6 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13+9x } & = & 6 \color{red}{ -9x }\color{blue}{+13+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-7}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7+13x } & = & 14 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &27x & = &21\\\Leftrightarrow & \color{red}{27}x & = &21\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{21}{27} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-x } & = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+14}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-5x } & = & 11 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+15}& = & 5 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-12x } & = & 5 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &5x & = &-18\\\Leftrightarrow & \color{red}{5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & 8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+15}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-x } & = & -1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &7x & = &-16\\\Leftrightarrow & \color{red}{7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & 3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-8}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x } & = & 9 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &27x & = &17\\\Leftrightarrow & \color{red}{27}x & = &17\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{17}{27} \\\Leftrightarrow & \color{green}{ x = \frac{17}{27} } & & \\ & V = \left\{ \frac{17}{27} \right\} & \\\end{align}\)