Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+7}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7+11x } & = & 12 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &25x & = &5\\\Leftrightarrow & \color{red}{25}x & = &5\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{5}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-12}& = & -10 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+5x } & = & -10 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+5}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5+7x } & = & 3 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-9}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9+13x } & = & -2 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &22x & = &7\\\Leftrightarrow & \color{red}{22}x & = &7\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{7}{22} \\\Leftrightarrow & \color{green}{ x = \frac{7}{22} } & & \\ & V = \left\{ \frac{7}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+12}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+13x } & = & 14 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &24x & = &2\\\Leftrightarrow & \color{red}{24}x & = &2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+14}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14+15x } & = & 10 \color{red}{ -15x }\color{blue}{-14+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+6}& = & 6 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-4x } & = & 6 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-14x & = &22\\\Leftrightarrow & \color{red}{-14}x & = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+7}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & 4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-13}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13+2x } & = & 2 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &9x & = &15\\\Leftrightarrow & \color{red}{9}x & = &15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)