Malcolm is trying a very low-carbohydrate diet. he would like to keep the amount of carbs consumed in grams between the levels shown in the following compound inequality:
50 < 2x + 10 and 2x + 10 < 110
solve for x in this inequality, and explain what the answer represents.
1. x < 20 and x > 50; malcolm needs to consume less than 20 grams of carbohydrates or more than 50 grams of carbohydrates.
2. x > 20 and x < 50; malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.
3. x > 30 and x < 60; malcolm needs to consume more than 30 grams of carbohydrates, but less than 60 grams of carbohydrates.
3. x < 30 and x > 60; malcolm needs to consume less than 30 grams of carbohydrates or more than 60 grams of carbohydrates.

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)