Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 120x-50x& = & 45+24 \\\Leftrightarrow & \color{red}{70} x& = & 69 \\\Leftrightarrow & x = \frac{69}{70} & & \\ & V = \left\{ \frac{69}{70} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{4})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{9}{4}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{48}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 48x \color{red}{+9} & = & \color{red}{20x} +9 \\\Leftrightarrow & 48x \color{red}{+9} \color{blue}{-9} \color{blue}{-20x} & = & \color{red}{20x} +9 \color{blue}{-20x} \color{blue}{-9} \\\Leftrightarrow & 48x-20x& = & 9-9 \\\Leftrightarrow & \color{red}{28} x& = & 0 \\\Leftrightarrow & x = \frac{0}{28} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{10}{11}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{+50} & = & \color{red}{165x} +66 \\\Leftrightarrow & 1100x \color{red}{+50} \color{blue}{-50} \color{blue}{-165x} & = & \color{red}{165x} +66 \color{blue}{-165x} \color{blue}{-50} \\\Leftrightarrow & 1100x-165x& = & 66-50 \\\Leftrightarrow & \color{red}{935} x& = & 16 \\\Leftrightarrow & x = \frac{16}{935} & & \\ & V = \left\{ \frac{16}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{10}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-110} & = & \color{red}{-693x} +42 \\\Leftrightarrow & 616x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & 616x+693x& = & 42+110 \\\Leftrightarrow & \color{red}{1309} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1309} & & \\ & V = \left\{ \frac{152}{1309} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{11})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{25}{11}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-25} & = & \color{red}{-44x} +6 \\\Leftrightarrow & -165x \color{red}{-25} \color{blue}{+25} \color{blue}{+44x} & = & \color{red}{-44x} +6 \color{blue}{+44x} \color{blue}{+25} \\\Leftrightarrow & -165x+44x& = & 6+25 \\\Leftrightarrow & \color{red}{-121} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-121} & & \\\Leftrightarrow & x = \frac{-31}{121} & & \\ & V = \left\{ \frac{-31}{121} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-12} & = & \color{red}{45x} +40 \\\Leftrightarrow & 120x \color{red}{-12} \color{blue}{+12} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{+12} \\\Leftrightarrow & 120x-45x& = & 40+12 \\\Leftrightarrow & \color{red}{75} x& = & 52 \\\Leftrightarrow & x = \frac{52}{75} & & \\ & V = \left\{ \frac{52}{75} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{5})& = & 8x+\frac{4}{7} \\\Leftrightarrow & 21x-\frac{14}{5}& = & 8x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{-98} & = & \color{red}{280x} +20 \\\Leftrightarrow & 735x \color{red}{-98} \color{blue}{+98} \color{blue}{-280x} & = & \color{red}{280x} +20 \color{blue}{-280x} \color{blue}{+98} \\\Leftrightarrow & 735x-280x& = & 20+98 \\\Leftrightarrow & \color{red}{455} x& = & 118 \\\Leftrightarrow & x = \frac{118}{455} & & \\ & V = \left\{ \frac{118}{455} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{12})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{25}{12}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+25} & = & \color{red}{-84x} +8 \\\Leftrightarrow & -120x \color{red}{+25} \color{blue}{-25} \color{blue}{+84x} & = & \color{red}{-84x} +8 \color{blue}{+84x} \color{blue}{-25} \\\Leftrightarrow & -120x+84x& = & 8-25 \\\Leftrightarrow & \color{red}{-36} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-36} & & \\\Leftrightarrow & x = \frac{17}{36} & & \\ & V = \left\{ \frac{17}{36} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{4})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{15}{4}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-45} & = & \color{red}{84x} +32 \\\Leftrightarrow & -120x \color{red}{-45} \color{blue}{+45} \color{blue}{-84x} & = & \color{red}{84x} +32 \color{blue}{-84x} \color{blue}{+45} \\\Leftrightarrow & -120x-84x& = & 32+45 \\\Leftrightarrow & \color{red}{-204} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-204} & & \\\Leftrightarrow & x = \frac{-77}{204} & & \\ & V = \left\{ \frac{-77}{204} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{7})& = & 3x+\frac{6}{7} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+16} & = & \color{red}{21x} +6 \\\Leftrightarrow & -140x \color{red}{+16} \color{blue}{-16} \color{blue}{-21x} & = & \color{red}{21x} +6 \color{blue}{-21x} \color{blue}{-16} \\\Leftrightarrow & -140x-21x& = & 6-16 \\\Leftrightarrow & \color{red}{-161} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-161} & & \\\Leftrightarrow & x = \frac{10}{161} & & \\ & V = \left\{ \frac{10}{161} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 8x-\frac{4}{5}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-8} & = & \color{red}{-30x} +45 \\\Leftrightarrow & 80x \color{red}{-8} \color{blue}{+8} \color{blue}{+30x} & = & \color{red}{-30x} +45 \color{blue}{+30x} \color{blue}{+8} \\\Leftrightarrow & 80x+30x& = & 45+8 \\\Leftrightarrow & \color{red}{110} x& = & 53 \\\Leftrightarrow & x = \frac{53}{110} & & \\ & V = \left\{ \frac{53}{110} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -4x+\frac{6}{11}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{+30} & = & \color{red}{495x} +66 \\\Leftrightarrow & -220x \color{red}{+30} \color{blue}{-30} \color{blue}{-495x} & = & \color{red}{495x} +66 \color{blue}{-495x} \color{blue}{-30} \\\Leftrightarrow & -220x-495x& = & 66-30 \\\Leftrightarrow & \color{red}{-715} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-715} & & \\\Leftrightarrow & x = \frac{-36}{715} & & \\ & V = \left\{ \frac{-36}{715} \right\} & \\\end{align}\)