Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{20}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-20} & = & \color{red}{49x} +6 \\\Leftrightarrow & -70x \color{red}{-20} \color{blue}{+20} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+20} \\\Leftrightarrow & -70x-49x& = & 6+20 \\\Leftrightarrow & \color{red}{-119} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-119} & & \\\Leftrightarrow & x = \frac{-26}{119} & & \\ & V = \left\{ \frac{-26}{119} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{3})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 10x-\frac{20}{3}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-60} & = & \color{red}{-81x} +10 \\\Leftrightarrow & 90x \color{red}{-60} \color{blue}{+60} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{+60} \\\Leftrightarrow & 90x+81x& = & 10+60 \\\Leftrightarrow & \color{red}{171} x& = & 70 \\\Leftrightarrow & x = \frac{70}{171} & & \\ & V = \left\{ \frac{70}{171} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 12x-\frac{9}{5}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{72}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-72} & = & \color{red}{200x} +25 \\\Leftrightarrow & 480x \color{red}{-72} \color{blue}{+72} \color{blue}{-200x} & = & \color{red}{200x} +25 \color{blue}{-200x} \color{blue}{+72} \\\Leftrightarrow & 480x-200x& = & 25+72 \\\Leftrightarrow & \color{red}{280} x& = & 97 \\\Leftrightarrow & x = \frac{97}{280} & & \\ & V = \left\{ \frac{97}{280} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{5})& = & 2x+\frac{7}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & 2x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{30x} +35 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{-30x} & = & \color{red}{30x} +35 \color{blue}{-30x} \color{blue}{-36} \\\Leftrightarrow & 135x-30x& = & 35-36 \\\Leftrightarrow & \color{red}{105} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{105} & & \\ & V = \left\{ \frac{-1}{105} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-18} & = & \color{red}{147x} +14 \\\Leftrightarrow & 84x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & 84x-147x& = & 14+18 \\\Leftrightarrow & \color{red}{-63} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-63} & & \\\Leftrightarrow & x = \frac{-32}{63} & & \\ & V = \left\{ \frac{-32}{63} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -20x-\frac{12}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-48} & = & \color{red}{196x} +63 \\\Leftrightarrow & -560x \color{red}{-48} \color{blue}{+48} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{+48} \\\Leftrightarrow & -560x-196x& = & 63+48 \\\Leftrightarrow & \color{red}{-756} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-756} & & \\\Leftrightarrow & x = \frac{-37}{252} & & \\ & V = \left\{ \frac{-37}{252} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+6} & = & \color{red}{-49x} +8 \\\Leftrightarrow & -63x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & -63x+49x& = & 8-6 \\\Leftrightarrow & \color{red}{-14} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-14} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{7})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -15x+\frac{12}{7}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+36} & = & \color{red}{-168x} +56 \\\Leftrightarrow & -315x \color{red}{+36} \color{blue}{-36} \color{blue}{+168x} & = & \color{red}{-168x} +56 \color{blue}{+168x} \color{blue}{-36} \\\Leftrightarrow & -315x+168x& = & 56-36 \\\Leftrightarrow & \color{red}{-147} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-147} & & \\\Leftrightarrow & x = \frac{-20}{147} & & \\ & V = \left\{ \frac{-20}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & -9x+\frac{5}{12} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-2376}{ \color{blue}{132} }x- \frac{216}{ \color{blue}{132} })& = & (\frac{-1188}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -2376x \color{red}{-216} & = & \color{red}{-1188x} +55 \\\Leftrightarrow & -2376x \color{red}{-216} \color{blue}{+216} \color{blue}{+1188x} & = & \color{red}{-1188x} +55 \color{blue}{+1188x} \color{blue}{+216} \\\Leftrightarrow & -2376x+1188x& = & 55+216 \\\Leftrightarrow & \color{red}{-1188} x& = & 271 \\\Leftrightarrow & x = \frac{271}{-1188} & & \\\Leftrightarrow & x = \frac{-271}{1188} & & \\ & V = \left\{ \frac{-271}{1188} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -462x+539x& = & 42-66 \\\Leftrightarrow & \color{red}{77} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{77} & & \\ & V = \left\{ \frac{-24}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 15x-\frac{15}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{-135} & = & \color{red}{693x} +88 \\\Leftrightarrow & 1485x \color{red}{-135} \color{blue}{+135} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{+135} \\\Leftrightarrow & 1485x-693x& = & 88+135 \\\Leftrightarrow & \color{red}{792} x& = & 223 \\\Leftrightarrow & x = \frac{223}{792} & & \\ & V = \left\{ \frac{223}{792} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{216x} +32 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{-216x} & = & \color{red}{216x} +32 \color{blue}{-216x} \color{blue}{-63} \\\Leftrightarrow & 336x-216x& = & 32-63 \\\Leftrightarrow & \color{red}{120} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{120} & & \\ & V = \left\{ \frac{-31}{120} \right\} & \\\end{align}\)