Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+12}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-11x } & = & -5 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-17\\\Leftrightarrow & \color{red}{-16}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-8}& = & 6 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8+2x } & = & 6 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-15}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-5x } & = & -2 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-17x & = &13\\\Leftrightarrow & \color{red}{-17}x & = &13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-14}& = & -7 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+3x } & = & -7 \color{red}{ -3x }\color{blue}{+14+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &10x & = &7\\\Leftrightarrow & \color{red}{10}x & = &7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-1}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1+13x } & = & 8 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &24x & = &9\\\Leftrightarrow & \color{red}{24}x & = &9\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{9}{24} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-12x & = &19\\\Leftrightarrow & \color{red}{-12}x & = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+10}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10+11x } & = & -2 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &23x & = &-12\\\Leftrightarrow & \color{red}{23}x & = &-12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{23} } & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+12}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-4x } & = & -1 \color{red}{ +4x }\color{blue}{-12-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -1 \color{blue}{-12} \\\Leftrightarrow &9x & = &-13\\\Leftrightarrow & \color{red}{9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-11}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-7x } & = & -1 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &8x & = &10\\\Leftrightarrow & \color{red}{8}x & = &10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)