Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-1}& = & 11 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-15x } & = & 11 \color{red}{ +15x }\color{blue}{+1-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-6x & = &4\\\Leftrightarrow & \color{red}{-6}x & = &4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+7}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-5x } & = & -14 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-21\\\Leftrightarrow & \color{red}{-17}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-3}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-5x } & = & 12 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &7x & = &15\\\Leftrightarrow & \color{red}{7}x & = &15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-5}& = & 2 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+10x } & = & 2 \color{red}{ -10x }\color{blue}{+5+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+8}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-5x } & = & -15 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-6x & = &-23\\\Leftrightarrow & \color{red}{-6}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+8}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x } & = & -9 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -9 \color{blue}{-8} \\\Leftrightarrow &17x & = &-17\\\Leftrightarrow & \color{red}{17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-17}{17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-5x & = &22\\\Leftrightarrow & \color{red}{-5}x & = &22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & -7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-13\\\Leftrightarrow & \color{red}{-16}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{16} } & & \\ & V = \left\{ \frac{13}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-3}& = & 14 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+x } & = & 14 \color{red}{ -x }\color{blue}{+3+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &2x & = &17\\\Leftrightarrow & \color{red}{2}x & = &17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-7x & = &13\\\Leftrightarrow & \color{red}{-7}x & = &13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)