Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+7}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+7x } & = & 9 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-7}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7+13x } & = & 1 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &27x & = &8\\\Leftrightarrow & \color{red}{27}x & = &8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-8}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-7x } & = & -2 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &8x & = &6\\\Leftrightarrow & \color{red}{8}x & = &6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+10}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10-13x } & = & -13 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & -6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+8}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-5x } & = & 12 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+4}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4-3x } & = & -7 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-2x & = &-11\\\Leftrightarrow & \color{red}{-2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-8}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-3x } & = & 6 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &-14x & = &14\\\Leftrightarrow & \color{red}{-14}x & = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & 14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+6}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-7x } & = & -7 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &2x & = &-13\\\Leftrightarrow & \color{red}{2}x & = &-13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+9}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-13x } & = & 15 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-19x & = &6\\\Leftrightarrow & \color{red}{-19}x & = &6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)