Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{9})& = & -2x+\frac{3}{7} \\\Leftrightarrow & 15x-\frac{20}{9}& = & -2x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-140} & = & \color{red}{-126x} +27 \\\Leftrightarrow & 945x \color{red}{-140} \color{blue}{+140} \color{blue}{+126x} & = & \color{red}{-126x} +27 \color{blue}{+126x} \color{blue}{+140} \\\Leftrightarrow & 945x+126x& = & 27+140 \\\Leftrightarrow & \color{red}{1071} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1071} & & \\ & V = \left\{ \frac{167}{1071} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{6}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-66} & = & \color{red}{539x} +42 \\\Leftrightarrow & 924x \color{red}{-66} \color{blue}{+66} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+66} \\\Leftrightarrow & 924x-539x& = & 42+66 \\\Leftrightarrow & \color{red}{385} x& = & 108 \\\Leftrightarrow & x = \frac{108}{385} & & \\ & V = \left\{ \frac{108}{385} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x- \frac{32}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{-32} & = & \color{red}{-198x} +99 \\\Leftrightarrow & -176x \color{red}{-32} \color{blue}{+32} \color{blue}{+198x} & = & \color{red}{-198x} +99 \color{blue}{+198x} \color{blue}{+32} \\\Leftrightarrow & -176x+198x& = & 99+32 \\\Leftrightarrow & \color{red}{22} x& = & 131 \\\Leftrightarrow & x = \frac{131}{22} & & \\ & V = \left\{ \frac{131}{22} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{9})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 20x+\frac{16}{9}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{112}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+112} & = & \color{red}{189x} +54 \\\Leftrightarrow & 1260x \color{red}{+112} \color{blue}{-112} \color{blue}{-189x} & = & \color{red}{189x} +54 \color{blue}{-189x} \color{blue}{-112} \\\Leftrightarrow & 1260x-189x& = & 54-112 \\\Leftrightarrow & \color{red}{1071} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{1071} & & \\ & V = \left\{ \frac{-58}{1071} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{5})& = & -4x+\frac{10}{3} \\\Leftrightarrow & -35x-\frac{14}{5}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{42}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-42} & = & \color{red}{-60x} +50 \\\Leftrightarrow & -525x \color{red}{-42} \color{blue}{+42} \color{blue}{+60x} & = & \color{red}{-60x} +50 \color{blue}{+60x} \color{blue}{+42} \\\Leftrightarrow & -525x+60x& = & 50+42 \\\Leftrightarrow & \color{red}{-465} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-465} & & \\\Leftrightarrow & x = \frac{-92}{465} & & \\ & V = \left\{ \frac{-92}{465} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{11})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -14x+\frac{21}{11}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1078}{ \color{blue}{77} }x+ \frac{147}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1078x \color{red}{+147} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -1078x \color{red}{+147} \color{blue}{-147} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{-147} \\\Leftrightarrow & -1078x+231x& = & 110-147 \\\Leftrightarrow & \color{red}{-847} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-847} & & \\\Leftrightarrow & x = \frac{37}{847} & & \\ & V = \left\{ \frac{37}{847} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{24}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{48}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-48} & = & \color{red}{-70x} +21 \\\Leftrightarrow & -168x \color{red}{-48} \color{blue}{+48} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{+48} \\\Leftrightarrow & -168x+70x& = & 21+48 \\\Leftrightarrow & \color{red}{-98} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-98} & & \\\Leftrightarrow & x = \frac{-69}{98} & & \\ & V = \left\{ \frac{-69}{98} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-54} & = & \color{red}{231x} +55 \\\Leftrightarrow & 990x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +55 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & 990x-231x& = & 55+54 \\\Leftrightarrow & \color{red}{759} x& = & 109 \\\Leftrightarrow & x = \frac{109}{759} & & \\ & V = \left\{ \frac{109}{759} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & -9x+\frac{9}{11} \\\Leftrightarrow & -4x+\frac{6}{11}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{+6} & = & \color{red}{-99x} +9 \\\Leftrightarrow & -44x \color{red}{+6} \color{blue}{-6} \color{blue}{+99x} & = & \color{red}{-99x} +9 \color{blue}{+99x} \color{blue}{-6} \\\Leftrightarrow & -44x+99x& = & 9-6 \\\Leftrightarrow & \color{red}{55} x& = & 3 \\\Leftrightarrow & x = \frac{3}{55} & & \\ & V = \left\{ \frac{3}{55} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{16}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+112} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 1540x \color{red}{+112} \color{blue}{-112} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-112} \\\Leftrightarrow & 1540x+693x& = & 110-112 \\\Leftrightarrow & \color{red}{2233} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{2233} & & \\ & V = \left\{ \frac{-2}{2233} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{11})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -8x+\frac{8}{11}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{+32} & = & \color{red}{396x} +33 \\\Leftrightarrow & -352x \color{red}{+32} \color{blue}{-32} \color{blue}{-396x} & = & \color{red}{396x} +33 \color{blue}{-396x} \color{blue}{-32} \\\Leftrightarrow & -352x-396x& = & 33-32 \\\Leftrightarrow & \color{red}{-748} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-748} & & \\\Leftrightarrow & x = \frac{-1}{748} & & \\ & V = \left\{ \frac{-1}{748} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 8x+\frac{6}{7} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-98} & = & \color{red}{168x} +18 \\\Leftrightarrow & 441x \color{red}{-98} \color{blue}{+98} \color{blue}{-168x} & = & \color{red}{168x} +18 \color{blue}{-168x} \color{blue}{+98} \\\Leftrightarrow & 441x-168x& = & 18+98 \\\Leftrightarrow & \color{red}{273} x& = & 116 \\\Leftrightarrow & x = \frac{116}{273} & & \\ & V = \left\{ \frac{116}{273} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-12 05:17:13
Een site van Busleyden Atheneum Mechelen