Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+7}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+8x } & = & -13 \color{red}{ -8x }\color{blue}{-7+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-11}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-9x } & = & 12 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-17x & = &23\\\Leftrightarrow & \color{red}{-17}x & = &23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+4}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+7x } & = & 15 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &19x & = &11\\\Leftrightarrow & \color{red}{19}x & = &11\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{11}{19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-x } & = & -6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-2}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-9x } & = & -10 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+3}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-9x } & = & 10 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x } & = & -8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+6}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6-10x } & = & 12 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)