Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{8}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{72}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-72} & = & \color{red}{693x} +44 \\\Leftrightarrow & -594x \color{red}{-72} \color{blue}{+72} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+72} \\\Leftrightarrow & -594x-693x& = & 44+72 \\\Leftrightarrow & \color{red}{-1287} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-1287} & & \\\Leftrightarrow & x = \frac{-116}{1287} & & \\ & V = \left\{ \frac{-116}{1287} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -90x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -90x+105x& = & 20+36 \\\Leftrightarrow & \color{red}{15} x& = & 56 \\\Leftrightarrow & x = \frac{56}{15} & & \\ & V = \left\{ \frac{56}{15} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{4})& = & 8x+\frac{7}{2} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{+15} & = & \color{red}{32x} +14 \\\Leftrightarrow & 60x \color{red}{+15} \color{blue}{-15} \color{blue}{-32x} & = & \color{red}{32x} +14 \color{blue}{-32x} \color{blue}{-15} \\\Leftrightarrow & 60x-32x& = & 14-15 \\\Leftrightarrow & \color{red}{28} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{28} & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+162} & = & \color{red}{-495x} +110 \\\Leftrightarrow & -1188x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +110 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & -1188x+495x& = & 110-162 \\\Leftrightarrow & \color{red}{-693} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-693} & & \\\Leftrightarrow & x = \frac{52}{693} & & \\ & V = \left\{ \frac{52}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{11})& = & 9x+\frac{2}{7} \\\Leftrightarrow & 28x+\frac{28}{11}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x+ \frac{196}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{+196} & = & \color{red}{693x} +22 \\\Leftrightarrow & 2156x \color{red}{+196} \color{blue}{-196} \color{blue}{-693x} & = & \color{red}{693x} +22 \color{blue}{-693x} \color{blue}{-196} \\\Leftrightarrow & 2156x-693x& = & 22-196 \\\Leftrightarrow & \color{red}{1463} x& = & -174 \\\Leftrightarrow & x = \frac{-174}{1463} & & \\ & V = \left\{ \frac{-174}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{11})& = & 4x+\frac{7}{8} \\\Leftrightarrow & -35x+\frac{35}{11}& = & 4x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x+ \frac{280}{ \color{blue}{88} })& = & (\frac{352}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{+280} & = & \color{red}{352x} +77 \\\Leftrightarrow & -3080x \color{red}{+280} \color{blue}{-280} \color{blue}{-352x} & = & \color{red}{352x} +77 \color{blue}{-352x} \color{blue}{-280} \\\Leftrightarrow & -3080x-352x& = & 77-280 \\\Leftrightarrow & \color{red}{-3432} x& = & -203 \\\Leftrightarrow & x = \frac{-203}{-3432} & & \\\Leftrightarrow & x = \frac{203}{3432} & & \\ & V = \left\{ \frac{203}{3432} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+6} & = & \color{red}{49x} +3 \\\Leftrightarrow & 56x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & 56x-49x& = & 3-6 \\\Leftrightarrow & \color{red}{7} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{6})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{588}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{24}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 588x \color{red}{+245} & = & \color{red}{-378x} +24 \\\Leftrightarrow & 588x \color{red}{+245} \color{blue}{-245} \color{blue}{+378x} & = & \color{red}{-378x} +24 \color{blue}{+378x} \color{blue}{-245} \\\Leftrightarrow & 588x+378x& = & 24-245 \\\Leftrightarrow & \color{red}{966} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{966} & & \\ & V = \left\{ \frac{-221}{966} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{2})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{15}{2}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{-105} & = & \color{red}{98x} +20 \\\Leftrightarrow & -126x \color{red}{-105} \color{blue}{+105} \color{blue}{-98x} & = & \color{red}{98x} +20 \color{blue}{-98x} \color{blue}{+105} \\\Leftrightarrow & -126x-98x& = & 20+105 \\\Leftrightarrow & \color{red}{-224} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-224} & & \\\Leftrightarrow & x = \frac{-125}{224} & & \\ & V = \left\{ \frac{-125}{224} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{11})& = & 2x+\frac{3}{5} \\\Leftrightarrow & 15x+\frac{10}{11}& = & 2x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+50} & = & \color{red}{110x} +33 \\\Leftrightarrow & 825x \color{red}{+50} \color{blue}{-50} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{-50} \\\Leftrightarrow & 825x-110x& = & 33-50 \\\Leftrightarrow & \color{red}{715} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{715} & & \\ & V = \left\{ \frac{-17}{715} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-66} & = & \color{red}{154x} +42 \\\Leftrightarrow & 1155x \color{red}{-66} \color{blue}{+66} \color{blue}{-154x} & = & \color{red}{154x} +42 \color{blue}{-154x} \color{blue}{+66} \\\Leftrightarrow & 1155x-154x& = & 42+66 \\\Leftrightarrow & \color{red}{1001} x& = & 108 \\\Leftrightarrow & x = \frac{108}{1001} & & \\ & V = \left\{ \frac{108}{1001} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{9})& = & 9x+\frac{5}{12} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{+32} & = & \color{red}{324x} +15 \\\Leftrightarrow & -288x \color{red}{+32} \color{blue}{-32} \color{blue}{-324x} & = & \color{red}{324x} +15 \color{blue}{-324x} \color{blue}{-32} \\\Leftrightarrow & -288x-324x& = & 15-32 \\\Leftrightarrow & \color{red}{-612} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-612} & & \\\Leftrightarrow & x = \frac{1}{36} & & \\ & V = \left\{ \frac{1}{36} \right\} & \\\end{align}\)