Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{7})& = & 3x+\frac{7}{3} \\\Leftrightarrow & 16x-\frac{8}{7}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-24} & = & \color{red}{63x} +49 \\\Leftrightarrow & 336x \color{red}{-24} \color{blue}{+24} \color{blue}{-63x} & = & \color{red}{63x} +49 \color{blue}{-63x} \color{blue}{+24} \\\Leftrightarrow & 336x-63x& = & 49+24 \\\Leftrightarrow & \color{red}{273} x& = & 73 \\\Leftrightarrow & x = \frac{73}{273} & & \\ & V = \left\{ \frac{73}{273} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -4x+\frac{10}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-176}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -176x \color{red}{+40} & = & \color{red}{-220x} +33 \\\Leftrightarrow & -176x \color{red}{+40} \color{blue}{-40} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-40} \\\Leftrightarrow & -176x+220x& = & 33-40 \\\Leftrightarrow & \color{red}{44} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{44} & & \\ & V = \left\{ \frac{-7}{44} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{360}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 360x \color{red}{-48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & 360x \color{red}{-48} \color{blue}{+48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{+48} \\\Leftrightarrow & 360x+100x& = & 45+48 \\\Leftrightarrow & \color{red}{460} x& = & 93 \\\Leftrightarrow & x = \frac{93}{460} & & \\ & V = \left\{ \frac{93}{460} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{11})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{4}{11}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{12}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-12} & = & \color{red}{-297x} +22 \\\Leftrightarrow & -264x \color{red}{-12} \color{blue}{+12} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{+12} \\\Leftrightarrow & -264x+297x& = & 22+12 \\\Leftrightarrow & \color{red}{33} x& = & 34 \\\Leftrightarrow & x = \frac{34}{33} & & \\ & V = \left\{ \frac{34}{33} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+40} & = & \color{red}{196x} +21 \\\Leftrightarrow & -168x \color{red}{+40} \color{blue}{-40} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-40} \\\Leftrightarrow & -168x-196x& = & 21-40 \\\Leftrightarrow & \color{red}{-364} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-364} & & \\\Leftrightarrow & x = \frac{19}{364} & & \\ & V = \left\{ \frac{19}{364} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{11})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 8x+\frac{8}{11}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+40} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 440x \color{red}{+40} \color{blue}{-40} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{-40} \\\Leftrightarrow & 440x+165x& = & 88-40 \\\Leftrightarrow & \color{red}{605} x& = & 48 \\\Leftrightarrow & x = \frac{48}{605} & & \\ & V = \left\{ \frac{48}{605} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 4x-\frac{8}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{-8} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 36x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & 36x+63x& = & 30+8 \\\Leftrightarrow & \color{red}{99} x& = & 38 \\\Leftrightarrow & x = \frac{38}{99} & & \\ & V = \left\{ \frac{38}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{11})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 25x+\frac{25}{11}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{275}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 275x \color{red}{+25} & = & \color{red}{-77x} +8 \\\Leftrightarrow & 275x \color{red}{+25} \color{blue}{-25} \color{blue}{+77x} & = & \color{red}{-77x} +8 \color{blue}{+77x} \color{blue}{-25} \\\Leftrightarrow & 275x+77x& = & 8-25 \\\Leftrightarrow & \color{red}{352} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{352} & & \\ & V = \left\{ \frac{-17}{352} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{9})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 16x-\frac{20}{9}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-220} & = & \color{red}{297x} +36 \\\Leftrightarrow & 1584x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +36 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & 1584x-297x& = & 36+220 \\\Leftrightarrow & \color{red}{1287} x& = & 256 \\\Leftrightarrow & x = \frac{256}{1287} & & \\ & V = \left\{ \frac{256}{1287} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -126x+147x& = & 14-30 \\\Leftrightarrow & \color{red}{21} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{21} & & \\ & V = \left\{ \frac{-16}{21} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{3})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -10x+\frac{8}{3}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+56} & = & \color{red}{-147x} +6 \\\Leftrightarrow & -210x \color{red}{+56} \color{blue}{-56} \color{blue}{+147x} & = & \color{red}{-147x} +6 \color{blue}{+147x} \color{blue}{-56} \\\Leftrightarrow & -210x+147x& = & 6-56 \\\Leftrightarrow & \color{red}{-63} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-63} & & \\\Leftrightarrow & x = \frac{50}{63} & & \\ & V = \left\{ \frac{50}{63} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{20}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+140} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -924x \color{red}{+140} \color{blue}{-140} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-140} \\\Leftrightarrow & -924x+385x& = & 22-140 \\\Leftrightarrow & \color{red}{-539} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-539} & & \\\Leftrightarrow & x = \frac{118}{539} & & \\ & V = \left\{ \frac{118}{539} \right\} & \\\end{align}\)