Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+12}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-11x } & = & 8 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-x } & = & 3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-16x & = &15\\\Leftrightarrow & \color{red}{-16}x & = &15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{16} } & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+14}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-5x } & = & -6 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-2}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-4x } & = & -14 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & -10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-21\\\Leftrightarrow & \color{red}{-3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-21}{-3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+1}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-7x } & = & 4 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-3}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+2x } & = & -5 \color{red}{ -2x }\color{blue}{+3+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-8}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-7x } & = & -4 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-x } & = & -8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)