Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14-x } & = & 1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &6x & = &15\\\Leftrightarrow & \color{red}{6}x & = &15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+7}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7+8x } & = & 14 \color{red}{ -8x }\color{blue}{-7+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & 9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-x } & = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7-x } & = & -6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &9x & = &-13\\\Leftrightarrow & \color{red}{9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-11}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-8x } & = & 8 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-9}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-5x } & = & -13 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+14}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-13x } & = & 1 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-19x & = &-13\\\Leftrightarrow & \color{red}{-19}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-13}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+7}& = & -13 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-4x } & = & -13 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-20\\\Leftrightarrow & \color{red}{-19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-20}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{20}{19} } & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)