Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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