Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -9x+\frac{9}{5}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{+81} & = & \color{red}{225x} +50 \\\Leftrightarrow & -405x \color{red}{+81} \color{blue}{-81} \color{blue}{-225x} & = & \color{red}{225x} +50 \color{blue}{-225x} \color{blue}{-81} \\\Leftrightarrow & -405x-225x& = & 50-81 \\\Leftrightarrow & \color{red}{-630} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-630} & & \\\Leftrightarrow & x = \frac{31}{630} & & \\ & V = \left\{ \frac{31}{630} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{2})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 21x+\frac{35}{2}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{105}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+105} & = & \color{red}{12x} +20 \\\Leftrightarrow & 126x \color{red}{+105} \color{blue}{-105} \color{blue}{-12x} & = & \color{red}{12x} +20 \color{blue}{-12x} \color{blue}{-105} \\\Leftrightarrow & 126x-12x& = & 20-105 \\\Leftrightarrow & \color{red}{114} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{114} & & \\ & V = \left\{ \frac{-85}{114} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{2})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -20x+\frac{15}{2}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{+165} & = & \color{red}{154x} +12 \\\Leftrightarrow & -440x \color{red}{+165} \color{blue}{-165} \color{blue}{-154x} & = & \color{red}{154x} +12 \color{blue}{-154x} \color{blue}{-165} \\\Leftrightarrow & -440x-154x& = & 12-165 \\\Leftrightarrow & \color{red}{-594} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{-594} & & \\\Leftrightarrow & x = \frac{17}{66} & & \\ & V = \left\{ \frac{17}{66} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{11})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 24x-\frac{24}{11}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{-216} & = & \color{red}{495x} +77 \\\Leftrightarrow & 2376x \color{red}{-216} \color{blue}{+216} \color{blue}{-495x} & = & \color{red}{495x} +77 \color{blue}{-495x} \color{blue}{+216} \\\Leftrightarrow & 2376x-495x& = & 77+216 \\\Leftrightarrow & \color{red}{1881} x& = & 293 \\\Leftrightarrow & x = \frac{293}{1881} & & \\ & V = \left\{ \frac{293}{1881} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{9})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+8} & = & \color{red}{81x} +7 \\\Leftrightarrow & 72x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +7 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & 72x-81x& = & 7-8 \\\Leftrightarrow & \color{red}{-9} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-9} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{25}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{75}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-75} & = & \color{red}{-231x} +88 \\\Leftrightarrow & -660x \color{red}{-75} \color{blue}{+75} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+75} \\\Leftrightarrow & -660x+231x& = & 88+75 \\\Leftrightarrow & \color{red}{-429} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-429} & & \\\Leftrightarrow & x = \frac{-163}{429} & & \\ & V = \left\{ \frac{-163}{429} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 4x+\frac{5}{2} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 4x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-396}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -396x \color{red}{-36} & = & \color{red}{88x} +55 \\\Leftrightarrow & -396x \color{red}{-36} \color{blue}{+36} \color{blue}{-88x} & = & \color{red}{88x} +55 \color{blue}{-88x} \color{blue}{+36} \\\Leftrightarrow & -396x-88x& = & 55+36 \\\Leftrightarrow & \color{red}{-484} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-484} & & \\\Leftrightarrow & x = \frac{-91}{484} & & \\ & V = \left\{ \frac{-91}{484} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -6x+\frac{12}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+84} & = & \color{red}{-539x} +66 \\\Leftrightarrow & -462x \color{red}{+84} \color{blue}{-84} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{-84} \\\Leftrightarrow & -462x+539x& = & 66-84 \\\Leftrightarrow & \color{red}{77} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{77} & & \\ & V = \left\{ \frac{-18}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{9})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{297x} +36 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{-297x} & = & \color{red}{297x} +36 \color{blue}{-297x} \color{blue}{+88} \\\Leftrightarrow & 396x-297x& = & 36+88 \\\Leftrightarrow & \color{red}{99} x& = & 124 \\\Leftrightarrow & x = \frac{124}{99} & & \\ & V = \left\{ \frac{124}{99} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -8x-\frac{6}{11}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-6} & = & \color{red}{-99x} +10 \\\Leftrightarrow & -88x \color{red}{-6} \color{blue}{+6} \color{blue}{+99x} & = & \color{red}{-99x} +10 \color{blue}{+99x} \color{blue}{+6} \\\Leftrightarrow & -88x+99x& = & 10+6 \\\Leftrightarrow & \color{red}{11} x& = & 16 \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{7})& = & 6x+\frac{7}{12} \\\Leftrightarrow & 25x+\frac{20}{7}& = & 6x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{2100}{ \color{blue}{84} }x+ \frac{240}{ \color{blue}{84} })& = & (\frac{504}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 2100x \color{red}{+240} & = & \color{red}{504x} +49 \\\Leftrightarrow & 2100x \color{red}{+240} \color{blue}{-240} \color{blue}{-504x} & = & \color{red}{504x} +49 \color{blue}{-504x} \color{blue}{-240} \\\Leftrightarrow & 2100x-504x& = & 49-240 \\\Leftrightarrow & \color{red}{1596} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{1596} & & \\ & V = \left\{ \frac{-191}{1596} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{1}{3})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 14x-\frac{7}{3}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{77}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-77} & = & \color{red}{165x} +18 \\\Leftrightarrow & 462x \color{red}{-77} \color{blue}{+77} \color{blue}{-165x} & = & \color{red}{165x} +18 \color{blue}{-165x} \color{blue}{+77} \\\Leftrightarrow & 462x-165x& = & 18+77 \\\Leftrightarrow & \color{red}{297} x& = & 95 \\\Leftrightarrow & x = \frac{95}{297} & & \\ & V = \left\{ \frac{95}{297} \right\} & \\\end{align}\)